Question

Is this correct???? I will give brainliest

Answer 1

$\frac{3}{4} \sqrt{-80}$

Step-by-step explanation:

Given data: $\frac{3}{4} \sqrt{-80}$

We find the equivalent value the expression $\frac{3}{4} \sqrt{-80}$.

The value –80 can be written as –1 × 16 × 5.

Now, substitute the value of –80 in the given expression.

$\frac{3}{4} \sqrt{-80}=\frac{3}{4} \sqrt{-1 \times 16 \times 5}$

       $=\frac{3}{4} \sqrt{-1 \times 4^{2} \times 5}$  (16 is the square number of 4)

       $=\frac{3}{4} \times 4 \sqrt{-1 \times 5}$  (Square number can be taken out)

       $=3 \sqrt{-1 \times 5}$ (4 in the numerator and denominator are cancel)

Since$\sqrt{-1}=i$,

       $=3i\sqrt{5}$  

So, the expression $\frac{3}{4} \sqrt{-80}$ is equivalent to $3i\sqrt{5}$.