Question

What is the square root of $700?$

Answer 1

Hint: We will use the identity $\sqrt{ab}=\sqrt{a}\sqrt{b}.$ We know that the given number is not a perfect square. But we can write it as a multiple of a perfect square. Then, we will use this identity to find the square root of the given number in a simplified form.

Complete step by step solution:
Let us consider the given number, $700.$
We are asked to find the square root of this number.
We know that the given number is not a perfect square. We need to write the given number as a multiple of a perfect square in order to simplify the given number to a further simplified radical form.
We know that $700=7\times 100.$
So, we will get $\sqrt{700}=\sqrt{7\times 100}.$
Now, we can use the identity given by $\sqrt{ab}=\sqrt{a}\sqrt{b}.$
Let us use the above identity, we will get $\sqrt{700}=\sqrt{7}\sqrt{100}.$
We know that the number $7$ is a prime number and so, it is not a perfect square. But the number $100$ is a perfect square. Also, we cannot write $7$ as a multiple of a perfect square. So, we will write it as it is.
We know that the square root of $100$ is $10.$ That is $\sqrt{100}=10.$
Therefore, we will get the square root of the given number as $\sqrt{700}=10\sqrt{7}.$
Hence the square root of $\sqrt{700}=10\sqrt{7}.$

Note: Let us find the approximate value of $\sqrt{7}$ in the decimal form. Then we can multiply it with $10.$ So, we will get the square root of $700$ in the decimal form. Since the simplified form of $\sqrt{700}$ contains a radical sign, this number is said to be in its radical form.