# How do you simplify root4(93)*sqrt(92)?

Jun 4, 2018

You can use logarithms if your calculator cannot do higher-order roots directly.
$29.787$

#### Explanation:

.^4√93⋅√92 = $\frac{1}{4} \log \left(93\right) + \frac{1}{2} \log \left(92\right)$

Logarithm tables are readily available online and in libraries.

$\frac{1}{4} \log \left(93\right) + \frac{1}{2} \log \left(92\right)$ = $\frac{1}{4} \left(1.9685\right) + \frac{1}{2} \left(1.9638\right)$

$0.4921 + 0.9819 = 1.4740$
To convert this back to the desired number, use the exponential function (inverse of logarithm):$\exp \left(1.4740\right) = {10}^{1.4740} = 29.787$

Direct calculator calculation:
$3.1054 \times 9.5917 = 29.787$