Question

S1. Find the value of √576 x √5.76​

Answer 1

Answer:

57.6

Step-by-step explanation:

We know that (√x)² = x

that is √x × √x = (√x)² = x

Let's just prove so that we can make it true

we know that

√x = x^(1/2)

√x × √x = x^(1/2) × x^(1/2)

we know x^m × x^n = x^m+n

so, x^(1/2) × x^(1/2) = x^((1/2) + (1/2)) = x¹ = x

√x × √x = x

Hence proved (Theorem 1)

also we should know that if √x × √y = √xy

Let's prove that also

√x × √y = x^(1/2) × y^(1/2)

we know that a^m × b^n = (a × b)^m

so,

x^(1/2) × y^(1/2) = (x × y)^(1/2)

= xy^(1/2) = √xy

Thus, √x × √y = √xy (Theorem 2)

Hence proved

So Now let's come back to the Question

√576 x √5.76

= √576 x √(576/100)

= √576 x (√576/√100)

From Theroem 1 and 2 we get

= (√576 x √576)/√100

= 576/√100

= 576/10

= 57.6

Hope you understood it........All the best