Question

If √x x √y = √xy , Find the products given below.

a. √3 x √12

b. √2 x √3

c. √5 x √10

d. √7 x √5​

Answer 1

answer is ( b )

√2×√3

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Answer 2

Given:

If √x x √y = √xy

To Find:

Find the products given below.

a. √3 x √12

b. √2 x √3

c. √5 x √10

d. √7 x √5​

Solution:

We are given with √x x √y = √xy and we need to find the values of the given expression, when we find the square root of any number we first prime factorize it and form pairs of each number and the pairs come out of the root.

(a)

$=\sqrt{3} *\sqrt{12} \\=\sqrt{36}\\=\sqrt{2*2*3*3}\\=2*3\\=6$

Hence, √3 x √12 is equal to 6.

(b)

$=\sqrt{2} *\sqrt{3} \\=\sqrt{3*2}\\=\sqrt{6}$

Hence, √2 x √3 is equal to √6.

(c)

$=\sqrt{5} *\sqrt{10} \\=\sqrt{50}\\=\sqrt{2*5*5}\\=5\sqrt{2}$

Hence, √5 x √10 is equal to 5√2.

(d)

$=\sqrt{7} *\sqrt{5} \\=\sqrt{35}$

Hence, √7 x √5​ is equal to √35.