Question

simplify the radical expression.

1. $(sqrt{13})(sqrt{26})$

Explanation:

Step1: Factor 26 into prime factors

$26 = 13 \times 2$, so rewrite the expression:
$(\sqrt{13})(\sqrt{13 \times 2})$

Step2: Use product property of radicals

$\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$, so expand the second radical:
$(\sqrt{13})(\sqrt{13} \times \sqrt{2})$

Step3: Multiply like radicals

$\sqrt{13} \times \sqrt{13} = 13$, so simplify:
$13 \times \sqrt{2}$

Answer:

$13\sqrt{2}$