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Square Root of 88

The square root of 88 is expressed as √88 in the radical form and as (88)^½ or (88)^0.5 in the exponent form. The square root of 88 rounded up to 7 decimal places is 9.3808315. It is the positive solution of the equation x² = 88. We can express the square root of 88 in its lowest radical form as 2 √22.

Square Root of 88: 9.38083151964686
Square Root of 88 in exponential form: (88)^½ or (88)^0.5
Square Root of 88 in radical form: √88 or 2 √22

1.	What Is the Square Root of 88?
2.	Is Square Root of 88 Rational or Irrational?
3.	How to Find the Square Root of 88?
4.	Important Notes on Square Root of 88
5.	Challenging Questions
6.	FAQs on Square Root of 88

What Is the Square Root of 88?

Finding the square root of a number, is the inverse process of squaring the number.
a × a = n ⇒ a² = n. Thus a = √n. √88 = √(a × a)
88 = 9.380 × 9.380 and 88 = - 9.380 × - 9.380.
√88 = ± 9.380
On prime factorization, we obtain 88 = 2 × 2 × 2 × 11. Thus √88 = 2 × 2 × 2 × 11
√88 = 2√22

Is Square Root of 88 Rational or Irrational?

√88 = 9.380831519646859 and thus we cannot express this as a rational number of the form p/q. This is a non-terminating decimal. Therefore, the square root of 88 is irrational.

How to Find the Square Root of 88?

The square root of 88 or any number can be calculated in many ways. Two of them are the approximation method and the long division method.

Square Root of 88 by Approximation Method

Take two perfect square numbers which are just smaller than 84 and just greater than 84. √81 < √84 < √100
9 < √ 88 < 10
Using the average method, divide 88 by 9 or 10.
Let us divide by 10⇒ 88 ÷ 10 = 8.8
Find the average of 8.8 and 10
(8.8 + 10) / 2 = 18.8 ÷ 2 = 9.4
√88 ≈ 9.4

Square Root of 88 by the Long Division Method

The long division method helps us to find a more accurate value of square root of any number. Let's see how to find the square root of by the long division method.

Write 88 as 88. 00 00 00. Find a number × number that gives the product 88 or less than that.
We determine 9 × 9 = 81. Subtract this from 88 and get the remainder as 7. Get down the pair of zeros down. 7 00 is our new dividend.
Double the quotient. We obtain 18. 18x is the new divisor. Find 18x × x such that the product is less than or equal to 7 00.
We determine that 183 × 3 = 5 49. Subtract this from 7 00 and obtain the remainder as 1 51. Bring down the next pair of zeros. 1 51 00 is the new dividend.
Double the quotient 9.3 ⇒ 186 and let us have 186x × x as our new divisor.
We determine 1868 × 8 = 1 49 44 as our product. Subtract this from 1 51 00. We obtain 1 56 as the remainder. Bring down the next pair of zeros.
Repeat the process until we obtain the quotient approximated to 3 decimal places.
√88 = ± 9.380

square root of 88 by division method

Explore Square roots using illustrations and interactive examples:

Important Notes

The square root of 88 is 9.380
The simplified form of radical form is 2√22
√88 is an irrational number.

Challenging Questions

Find the square root of : three-fourth of a square of a number that is equal to 5808.
What will be the least number multiplied with 88 to make it a perfect cube?

Square Root of 88 Solved Examples

Example 1: Ron is trying to build a square tower with the blocks with the base of 44 blocks. He has so far raised the tower by 2 layers. How many more blocks does he need to complete the square tower?

Solution:

Number of blocks × number of layers = total blocks
44 × 2 = 88 blocks
88 = 2 × 2 × 22
22 doesn't have a pair. To complete the square, 22 should be multiplied with 88.
88 × 22 = 2 × 2 × 22 × 22 = 1936
1936 blocks are needed to build the square tower which is the perfect square of 44.
He needs build 44 layers of 44 blocks.
He has used 88 blocks out of 1936 blocks. He needs 1848 more blocks.
Example 2: Evaluate: √88 ×√198

Solution:

√88 = √(2 × 2 × 2 × 11) = 2√22
√198 = √(2× 3 × 3 × 11) = 3√22
√88 ×√198 = 2√22 × 3√22 = 2 × 3 × √22 × √22
= 6 ×22 = 132
√88 ×√198 = 132
Example: If the area of a circle is 88π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 88π in²
⇒ r = ±√88 in
Since radius can't be negative,
⇒ r = √88
The square root of 88 is 9.381.
⇒ r = 9.381 in

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FAQs on the Square Root of 88

What is the Value of the Square Root of 88?

The square root of 88 is 9.38083.

Why is the Square Root of 88 an Irrational Number?

Upon prime factorizing 88 i.e. 2³ × 11¹, 2 is in odd power. Therefore, the square root of 88 is irrational.

Is the number 88 a Perfect Square?

The prime factorization of 88 = 2³ × 11¹. Here, the prime factor 2 is not in the pair. Therefore, 88 is not a perfect square.

Evaluate 4 plus 4 square root 88

The given expression is 4 + 4 √88. We know that the square root of 88 is 9.381. Therefore, 4 + 4 √88 = 4 + 4 × 9.381 = 4 + 37.523 = 41.523

What is the Square of the Square Root of 88?

The square of the square root of 88 is the number 88 itself i.e. (√88)² = (88)^2/2 = 88.

What is the Value of 13 square root 88?

The square root of 88 is 9.381. Therefore, 13 √88 = 13 × 9.381 = 121.951.

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