# Difference between revisions of "1976 AHSME Problems/Problem 27"

(Created page with "== Problem 27 == If <math>N=\frac{\sqrt{\sqrt{5}+2}+\sqrt{\sqrt{5}-2}}{\sqrt{\sqrt{5}+1}}-\sqrt{3-2\sqrt{2}}</math>, then <math>N</math> equals <math>\textbf{(A) }1\qquad \t...") |
(→Problem 27) |
||

Line 8: | Line 8: | ||

\textbf{(D) }\sqrt{\frac{5}{2}}\qquad | \textbf{(D) }\sqrt{\frac{5}{2}}\qquad | ||

\textbf{(E) }\text{none of these} </math> | \textbf{(E) }\text{none of these} </math> | ||

+ | |||

+ | ==Solution== | ||

+ | |||

+ | We will split this problem into two parts: The fraction on the left and the square root on the right. | ||

+ | |||

+ | Starting with the fraction on the left, begin by squaring the numerator and putting a square root around it. It becomes <math>\frac{\sqrt{(\sqrt{\sqrt{5}+2}+\sqrt{\sqrt{5}-2})^2}}{\sqrt{\sqrt{5}+1}}</math> |

## Revision as of 17:56, 20 March 2020

## Problem 27

If , then equals

## Solution

We will split this problem into two parts: The fraction on the left and the square root on the right.

Starting with the fraction on the left, begin by squaring the numerator and putting a square root around it. It becomes