Is 176 a perfect square? If not, find the smallest number by which it should be multiplied to get a perfect square.
Solution:
Given, the number is 176.
We have to determine if 176 is a perfect square or not.
Prime factorization is a way of expressing a number as a product of its prime factors.
A prime number is a number that has exactly two factors, 1 and the number itself.
Using prime factorisation,
So, 176 = 2 × 2 × 2 × 2 × 11
We observe that 11 occurs without a pair.
Therefore, 176 is not a perfect square.
We have to determine the smallest number by which 176 should be multiplied to get a perfect square.
176 should be multiplied by 11.
So, 176 × 11 = 1936
Factors of 1936 = 2 × 2 × 2 × 2 × 11 × 11
= √1936
= √(2² × 2² × 11²)
= 2 × 2 × 11
= 44
Therefore, the smallest number to be multiplied is 11.
✦ Try This: Is 396 a perfect square? If not, find the smallest number by which it should be multiplied to get a perfect square.
☛ Also Check: NCERT Solutions for Class 8 Maths
NCERT Exemplar Class 8 Maths Chapter 3 Problem 98
Is 176 a perfect square? If not, find the smallest number by which it should be multiplied to get a perfect square
Summary:
176 is not a perfect square. The smallest number by which 176 should be multiplied to get a perfect square is 11.
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