
What is the square root of
Answer
457.5k+ views
Hint: We will use the identity 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,
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
So, we will get
Now, we can use the identity given by
Let us use the above identity, we will get
We know that the number is a prime number and so, it is not a perfect square. But the number is a perfect square. Also, we cannot write as a multiple of a perfect square. So, we will write it as it is.
We know that the square root of is That is
Therefore, we will get the square root of the given number as
Hence the square root of
Note: Let us find the approximate value of in the decimal form. Then we can multiply it with So, we will get the square root of in the decimal form. Since the simplified form of contains a radical sign, this number is said to be in its radical form.
Complete step by step solution:
Let us consider the given number,
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
So, we will get
Now, we can use the identity given by
Let us use the above identity, we will get
We know that the number
We know that the square root of
Therefore, we will get the square root of the given number as
Hence the square root of
Note: Let us find the approximate value of
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