Question

How do you simplify $\sqrt{88}?$

Answer 1

Hint: We need to simplify the square root of 88. We start to solve the given question by expressing the number 88 as the product of prime factors. Then, we look for perfect squares in the prime factors and simplify the expression to get the desired result.

Complete step by step solution:
We need to simplify the square root of 88. We will be solving the given question by expressing the number 88 as the product of prime factors.
Prime factorization is used to express a number by the product of prime numbers. It is a method of finding all the prime factors which are multiplied to get the original number.
We know that the number 88 is expressed as the product of 2 and 44.
Writing the same, we get,
$\Rightarrow 88=2\times 44$
44 is a composite number and we can express it as the product of 2 and 22.
Writing the same, we get,
$\Rightarrow 88=2\times 2\times 22$
22 is a composite number and we can express it as the product of 2 and 11.
$\Rightarrow 88=2\times 2\times 2\times 11$
11 is a prime number. So, the above expression cannot be further simplified.
The number 88 is expressed as the product of prime factors as follows,
$\Rightarrow 88=2\times 2\times 2\times 11$
Substituting the above expression in the square root, we get,
$\Rightarrow \sqrt{88}=\sqrt{2\times 2\times 2\times 11}$
Expressing the above expression as the product of perfect square, we get,
$\Rightarrow \sqrt{88}=\sqrt{\left( 2\times 2 \right)\times \left( 2\times 11 \right)}$
In the above equation, $\left( 2\times 2 \right)$ is a perfect square.
Taking the perfect squares out of the square root,
$\Rightarrow \sqrt{88}=2\sqrt{\left( 2\times 11 \right)}$
Simplifying the above equation, we get,
$\therefore \sqrt{88}=2\sqrt{22}$

Note: We can verify the result of the question using the equation
$\sqrt{88}=2\sqrt{22}$
 . The result of the given question can be cross-checked as follows,
LHS:
$\Rightarrow \sqrt{88}$
RHS:
$\Rightarrow 2\sqrt{22}$
Taking the number $2$ inside the square root, we get,
$\Rightarrow \sqrt{2\times 2\times 22}$
$\Rightarrow \sqrt{4\times 22}$
$\Rightarrow \sqrt{88}$
$\therefore$ LHS $=\;$ RHS. The result attained is correct.