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What is the square root of 961?

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Last updated date: 29th Feb 2024
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IVSAT 2024
Answer
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Hint: In this problem, we have to find the square root of 961. We should know that every positive number has two square roots, one positive and one negative. If we only want the positive square root of a positive number then we use a radical sign, \[\sqrt{m}\], which denotes the positive square root of m. Here we have a perfect square number for which we can find the simplest radical form.

Complete step by step answer:
We know that the given square root is,
 \[\sqrt{961}\]
Here we have to find its simplest radical form.
We know that 961 is the 31 squared, we can now write it as,
\[\Rightarrow \sqrt{{{\left( 31 \right)}^{2}}}\]
We can now write the radical symbol in terms of exponent, we get
\[\Rightarrow {{\left( 31 \right)}^{\dfrac{1}{2}\times 2}}\]
Here, we can now cancel the radical symbol square root which represent half in the exponent and the square inside the square root, we get
\[\Rightarrow 31\]
Therefore, the square root of 961 is 31.

Note: Students should remember some of the perfect square numbers to simplify these types of problems. We should remember that we can now cancel the radical symbol square root which represents half in the exponent and the square inside the square root. We should know that If we only want the positive square root of a positive number then we use a radical sign, \[\sqrt{m}\], which denotes the positive square root of m. we should know that, the square root of 169 is 13 and the square root of 961 is 31 (which is inverted).