Square Root Of 9 100

Square root of eighteen is equal to three√2 in radical form and 4.24264068712 in decimal class. When we multiply the value of the square root of a number to itself, it produces the original number. Therefore, square root is the changed or contrary procedure of squaring a number. If √18 = x, then x² = eighteen.

The square root of eighteen is denoted by √xviii, where '√' is the radical symbol and 18 is the radicand.

Since, √2 is an irrational number, therefore, √18 = 3√ii is also an irrational number. Therefore, we cannot represent the square root of the irrational number in the form of P/Q, where P is the numerator and Q is the denominator.

Square root of 18 = √eighteen = ±iii√2

In decimal form,

√18 = 4.24264068712

In Exponent Form,

(18)^½ = iv.24264068712

The number eighteen is not a perfect square, hence the foursquare root of xviii will non be a whole number. Besides, we cannot determine the exact value of √18, using prime factorisation. Therefore, we tin use the long sectionalization method to find the value of √18.

How to Find the Square root of 18?

We can detect the foursquare root using these methods:

Prime Factorisation Method
Long Segmentation Method

Prime Factorisation Method

By the prime factorisation method, nosotros can write:

xviii = 2 10 three x 3

Now, let us see how many prime factors can exist paired to make square terms.

18 = 2 x (iii x iii)

Now, we can represent 3 ten three = iii². Hence,

18 = 2 10 3²

Taking square root on both the sides, we get;

\(\brainstorm{assortment}{l}\sqrt{xviii} = \sqrt{2\times 3^{2}}\end{assortment} \)

Nosotros tin cancel the square term with the square root.

√18 = 3√2

Thus, this is the value of √eighteen, in radical form.

Since, the value of √two = 1.4142135624

Therefore, iii√2 = iii 10 1.4142135624 = 4.24264068712

Finally, the value of square root of 18 is:

√xviii = 4.24264068712

Which is an irrational number.

Facts:

Foursquare root of 18 is a not a natural or a whole number merely an irrational number
18 is an even composite number
eighteen is an imperfect square, hence no natural number tin can be squared to go the original number
eighteen is a multiple of 2, 3, half dozen, 9 and xviii itself
The roots of 18 are +3√ii or -3√two

Long Division Method

This is the quick method to find the square root of xviii, accurately. Nosotros tin apply this method to determine the value of √18 upwards to four places of decimals. Permit us run into the steps that are involved in the long division method.

Step 1: We can write the number eighteen every bit 18.00 00 00 00
Step 2: Now, we have to group the numbers in a pair of two.
Step three: We demand to divide 18 by such a number that when it is multiplied past itself, it generates a value less than or equal to 18. Thus, four ten 4 = 16
Step four: Subsequently dividing 18 by 4, we are left with a remainder equal to 2 and the divisor will go eight. Now, have downwards the next pair of numbers and combine with 2 to become 200, as shown in the figure.
Step 5: Again combining the divisor viii with such a number, such that the multiplication will result in a value less than or equal to the new dividend, i.due east. 200.

82 x two = 164

Step 6: Now, the divisor is 82 + 2 = 84 and remainder is 36. Repeat the method again up to four places of decimal.

Square root of 18

Therefore, the square root of 18 is equal to 4.2426, approximately.

Approximation Method

Some other most unlikely method of finding the foursquare root of any number is the approximation method. With this method, nosotros tin can find the judge square root of whatever number only not the exact value.

Suppose we are finding the square root of eighteen using this method, then:

18 lies between 4² = 16 and five^two = 25

Thus, the square root of xviii is more than four but less than 5, and so we got the initial value.

Now, we need to find the decimal part.

Decimal part = (Actual number- Lower perfect square) /(Higher perfect foursquare-Lower perfect square)

= (18-xvi)/(25-16)

= 2/9

= 0.22

Therefore, the value of √18 = iv.22

Repeated Subtraction Method

We cannot use the repeated subtraction method here to find the foursquare root of 18. This method is applicable only if a number is a perfect square but 18 is an imperfect square. To check we can try this method here.

Basically, in this method, the bodily number is repeatedly subtracted with the sequent odd numbers, till we get a departure equal to zero. Starting with the actual number, nosotros subtract it with 1, then the resulting value is subtracted with the adjacent odd number, i.e. iii and and then on.

xviii – i = 17
17 – 3 = 14
fourteen – 5 = nine
9 – 7 = ii
2 – nine = -seven

Since, we didn't become goose egg in any step of the subtractions done above, therefore, we cannot find the square root of 18 here. Hence, the method is not applicable.

Foursquare Roots of Numbers

Square root of 28 = 5.29150262213
Square root of 3 = 1.73205080757
Square root of 6 = two.44948974278
Square root of 7 = 2.64575131106
Square root of eight = two.82842712475
Foursquare root of 9 = 3
Foursquare root of 40 = six.32455532034
Foursquare root of 49 = 7
Square root of 180 = 13.416407865

Video Lessons on Foursquare Roots

Visualising square roots

Finding Square roots

Solved Examples

Q.1: Notice the foursquare root of 100/18.

Solution: Given, 100/18

Suppose the square root of 100/18 is x

X = √(100/eighteen)

X = √100/√18

√100 = 10

√18 = iii√two

10 = ten/(3√ii)

We tin can further rationalize the denominator.

\(\brainstorm{array}{l}10 =\frac{10}{3\sqrt{2}}\times \frac{\sqrt{2}}{\sqrt{2}}\\ \frac{10\sqrt{ii}}{three\times 2}\\ \frac{v\sqrt{2}}{3}\end{array} \)

Q.2: Find the area of a chessboard whose side is equal to three√2 cm, each.

Solution: Given, the side of the chessboard is 3√ii cm.

Every bit we know, the chessboard is in foursquare shape. Therefore,

Surface area of the chessboard = (length of the side)²

Area = (3√2)²

Area = xviii sq.cm.

Therefore, the surface area of the chessboard is 18 sq.cm.

Q.3: What is the value of (√xviii)³?

Solution: The value of (√xviii)^three is:

(√18)³ = (iii√2)³

= 3³ x (√2)³

= 27 x 2√2

= 54√2

Practice Questions

√eighteen + √2 – 3√two = ?
How to write the square root of eighteen in radical form?
Betwixt which two whole numbers, the square root of 18 lies?
√18 divided by 3√ii is equal to _______.
What is the multiplicative inverse of √18?

Annals with us and download BYJU'Due south – The Learning App to learn more nigh squares and square roots with the assist of interactive videos.

Frequently Asked Questions on Square root of 18

What is the square root of eighteen?

The square root of eighteen is equal to 3√2 or four.2426 (up to four places of decimals).

Is 18 a perfect square?

No, eighteen is not a perfect square.The foursquare root of eighteen is not a whole number.

Is √18 a rational or irrational number?

√xviii is an irrational number.

What is the foursquare root of 18 simplified?

The square root of eighteen in simplest form is 3√2.

What is the square of 18?

The square of 18 is:
18² = 18 x 18 = 324

Is 18 a perfect cube?

xviii is non a perfect cube because the cube root of 18 is non a natural number.