+0

# non-integer square roots

-5
128
1
+-280

What is the value of $n$ such that \$$$10^n = 10^{-5}\times \sqrt{\frac{10^{73}}{0.001}}?$$

Apr 3, 2020

#1
+4599
+1

Recognize that 0.001 is $$10^{-3}$$.

$$\sqrt{10^{76}}$$=$$10^{38}$$.

Thus, $$10^n=10^{-5}*10^{38}=10^{33}.$$

n = 33.

Apr 3, 2020