Surds And Indices

To simplify $%5Csqrt%7B54-%5Csqrt%7B20%2B%5Csqrt%7B32-%5Csqrt%7B49%7D%7D%7D%7D$ , we follow these steps:

Step 1: Simplify the innermost expression, $%5Csqrt%7B49%7D$ . Since $49%3D7%5E2$ , we have $%5Csqrt%7B49%7D%3D7$ .

Step 2: Substitute back into the expression: $%5Csqrt%7B32-%5Csqrt%7B49%7D%7D%20%3D%20%5Csqrt%7B32-7%7D%20%3D%20%5Csqrt%7B25%7D$ . Knowing $25%3D5%5E2$ , we simplify to $%5Csqrt%7B25%7D%3D5$ .

Step 3: Substitute again: $%5Csqrt%7B20%2B%5Csqrt%7B32-%5Csqrt%7B49%7D%7D%7D%20%3D%20%5Csqrt%7B20%20%2B%205%7D%20%3D%20%5Csqrt%7B25%7D$ , and $%5Csqrt%7B25%7D%3D5$ .

Step 4: Finally, substitute one last time: $%5Csqrt%7B54-%5Csqrt%7B20%2B%5Csqrt%7B32-%5Csqrt%7B49%7D%7D%7D%7D%20%3D%20%5Csqrt%7B54-5%7D%20%3D%20%5Csqrt%7B49%7D$ , and so $%5Csqrt%7B49%7D%3D7$ .

Therefore, the simplified value is $7$ .

High-Yield Trend

Chapter Questions
1 MCQs

Official Solution

Surds And Indices

High-Yield Trend

Chapter Questions 1 MCQs

Official Solution

Chapter Questions
1 MCQs