Final answer:
To solve the square root of 470/20-1, simplify the expression by factoring the numbers inside the square roots, canceling out any common factors, and subtracting 1.
Step-by-step explanation:
To solve this problem, we need to simplify the expression first. To simplify the square root of 470/20-1, we can simplify the numerator and denominator separately. The square root of 470 can be written as sqrt(470), and the square root of 20 can be written as sqrt(20). Simplifying the expression, we get sqrt(470)/sqrt(20) - 1.
Next, we can simplify the square roots by factoring the numbers inside the square roots. The factors of 470 are 2 * 5 * 47, and the factors of 20 are 2 * 2 * 5. Simplifying further, we get (sqrt(2 * 5 * 47))/(sqrt(2 * 2 * 5)) - 1, which can be simplified to (sqrt(2) * sqrt(5) * sqrt(47))/(sqrt(2) * 2 * sqrt(5)) - 1.
Finally, we can cancel out the square roots of 2 and 5, resulting in sqrt(47)/2 - 1 as the final answer.