Question

If the number under the square root radical has no perfect souare

Answer 1

Answer:

true

Step-by-step explanation:

Examples :

180 = 5 × 2² × 3²

Then

The number 180 has perfect square factors which are 2 and 3

Then

The number √180 can be simplified because:

$\sqrt{180} =\sqrt{5\times 2^{2}\times 3^{2}}$

        $=\sqrt{5\times \left( 2\times 3\right)^{2} }$

        $=\sqrt{5\times \left( 6\right)^{2} }$

        $=\sqrt{5} \times \sqrt{6^{2}}$

        $=6\sqrt{5}$

On the other hand :

10 = 5 × 2

Then

The number 10 has no perfect square factors

Then

The number √10 cannot be simplified because:

$\sqrt{10} =\sqrt{5\times 2} =\sqrt{5} \times \sqrt{2}$

$\text{and} \ \sqrt{5} \times \sqrt{2} \ \text{is not a simplified expression of} \ \sqrt{10} \ \\\text{,in fact it is more complicated than} \ \sqrt{10}$