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CTET Paper II (Mathematics and Science) 17 Jan 2022 Solved Paper

Question : 31 of 150

Marks: +1, -0

The value of

\frac{\sqrt{768}\times \sqrt{3267}}{\sqrt{144}}

Solution:

Concept:

Simplify the expression by finding the square roots of each number using prime factorization.

Explanation:

First, factorize each number.

768 = 2^8 \times 3

, so

\sqrt{768} = 16\sqrt{3}

3267 = 3^3 \times 11^2

, so

\sqrt{3267} = 33\sqrt{3}

144 = 12^2

, so

\sqrt{144} = 12

Now multiply the square roots:

16\sqrt{3} \times 33\sqrt{3} = 16 \times 33 \times 3 = 1584

Divide by

12

1584 \div 12 = 132

Answer:

C. 132

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