Question

If
$if \: \sqrt{6} \times \sqrt{15} = x \: \sqrt{10} \: \: then \: the \: value \: of \: x \: \: is$
​

Answer 1

Answer:

3

Step-by-step explanation:

As per the provided information in the given question, we have :

$\longmapsto \rm {\sqrt{6} \times \sqrt{15} = x\sqrt{10} }$

We are asked to calculate the values of x.

In order to find the value of x. Firstly, we have to simply in the L.H.S. Then, by comparing L.H.S and R.H.S, we can find the value of x.

$\longmapsto \rm {\sqrt{6} \times \sqrt{15} = x\sqrt{10} }$

As we know that,

• $\bf {\sqrt{a} \times \sqrt{b} = \sqrt{ab} }$

$\longmapsto \rm {\sqrt{6 \times 15} = x\sqrt{10} }$

Now, performing multiplication under root.

$\longmapsto \rm {\sqrt{90} = x\sqrt{10} }$

Now, we'll find the square root of 90. By prime factorization, we get that 90 = 10 × 3 × 3, putting the sign of radical on both sides, √90 = √(10 × 3 × 3) ⇒ 3√10.

So, we can write √90 as,

$\longmapsto \rm { \bf{3} \rm \sqrt{10} =\bf{ x}\rm \sqrt{10} }$

On comparing L.H.S and R.H.S, we get,

$\longmapsto \bf {3 = x }$

∴ Value of x is 3.

Points to remember :

• (√a)² = a

• √a√b = √ab

• √a/√b = √a/b

• (√a + √b)(√a - √b) = a - b

• (a + √b)(a - √b) = a² - b

• (√a ± √b)² = a ± 2√ab + b

• (√a + √b)(√c + √d) = √ac + √ad + √bc + √bd