Using prime factorisation, find the square root of 11025.
Solution:
Given, the number is 11250.
We have to determine the square root of 11250 using prime factorisation.
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, 11250 = 3 × 3 × 5 × 5 × 7 × 7
We observe that 3, 5 and 7 occur in pairs.
Square root is an inverse operation of the square.
So, √11250 = √(3² × 5² × 7²)
= 3 × 5 × 7
= 105
Therefore, the square root of 11025 is 105.
✦ Try This: Using prime factorisation, find the square root of 5184.
☛ Also Check: NCERT Solutions for Class 8 Maths
NCERT Exemplar Class 8 Maths Chapter 3 Problem 96 (a)
Using prime factorisation, find the square root of 11025
Summary:
Using prime factorisation, the square root of 11025 is 105.
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