The square root of 117 in simplified radical form is 3√13. Mathematically, the square root of 117 can be expressed as √117. In this post, we will learn how to find the square root of 117 in its simplest form.
The formula of root 117 simplified is given below:
√117 = 3√13.
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Square root of 117 in Simplest Radical Form
Answer: 3√13 is the simplest radical form of square root 117.
Solution:
To find the square root of 117 in its simplest radical form, we will write 117 as a product of two numbers; at least one of them will be a perfect square.
A few perfect squares are 1, 4, 9, 16, 25, etc. Note that 9 divides 117, and we write 117 as
117 = 9 × 13.
Taking square root on both sides, we get that
$\sqrt{117}=\sqrt{9 \times 117}$
⇒ $\sqrt{117}$ $=\sqrt{9} \times \sqrt{117}$ using the formula √(a×b) = √a × √b.
= 3 × √13 as we know that the square root of 9 is 3.
= 3√13
Therefore, the square root of 117 in simplified radical form is equal to 3√13.
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FAQs on Square Root of 117
Answer: Note that 117 can be factored as 117 = 3 × 3 × 13. Thus, the square root of 117 is equal to √(3 × 3 × 13) = 3√13. So 3√13 is the simplified radical form of square root of 117.
