# How do you multiply sqrt(5)*5?

Jun 4, 2015

You cannot multiply it without decimal expression.
The rule for roots' product is, the outer ones with the outer ones, and the inner oines with the inner ones.
In this case there's only one inner and one outer, so the result is $5 \sqrt{5}$, if you decompose $\sqrt{5}$ in decimal expression, the product gives:
$5 \sqrt{5} = 11.18034$

Jun 4, 2015

Whatever you do, you will end up with either an approximation, or an expression involving square roots or fractional exponents.

What you can do is to move the second $5$ inside the square root, by squaring it...

$\sqrt{5} \cdot 5 = \sqrt{5} \cdot \sqrt{5 \cdot 5} = \sqrt{5 \cdot 5 \cdot 5} = \sqrt{125}$

...using $\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}$