Question #94618
2 Answers
Approximate form:
Explanation:
Prime factorize
Group the same prime factors into pairs.
Rewrite each pair in exponent form.
Apply the rule:
Simplify.
Simplify the square root (by "splitting" then solving), and approximate if needed:
Explanation:
A rule about exponents is that raising a product to a power, is the same as taking the product of each multiplier having been raised to the same power:
And the square root of a number can be rewritten as the same number raised to an exponent of
Why is that? Well, when we say square root, we mean a number where:
So if we rewrite
And
Shouldn't it be that
If
This rule is important here! It tells us that we can somehow "split" the square root of a product!
Now back to our problem:
Well,
Unfortunately, we can't simplify this any further, but we can approximate
So:
Pay attention to the squiggly lines; it indicates an approximation! So if they ask for an exact value, just give