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CTET Paper II (Mathematics and Science) May 2016 Solved Paper

Question : 57 of 150

Marks: +1, -0

\sqrt{768}×\sqrt{3267}

= 44 × y, then the value of y:

Solution:

Concept:

Use prime factorization to simplify the product of square roots, then apply

\sqrt{a} \times \sqrt{b} = \sqrt{a \times b}

and

\sqrt{a^m} = a^{m/2}

Explanation:

Factorize

768 = 256 \times 3 = 2^8 \times 3

Factorize

3267 = 121 \times 27 = 11^2 \times 3^3

So,

\sqrt{768} \times \sqrt{3267} = \sqrt{2^8 \times 3 \times 11^2 \times 3^3}

Combine powers of

3

3 \times 3^3 = 3^4

Thus, the product inside the square root is

2^8 \times 3^4 \times 11^2

Take square root:

\sqrt{2^8 \times 3^4 \times 11^2} = 2^{8/2} \times 3^{4/2} \times 11^{2/2} = 2^4 \times 3^2 \times 11

Compute:

2^4 = 16

3^2 = 9

, so

16 \times 9 \times 11 = 1584

Given

44 \times y = 1584

, so

y = 1584 \div 44 = 36

Answer:

36

(Option D)

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