Problem 109
Question
Evaluate each expression. $$\sqrt[3]{\sqrt[4]{16}+\sqrt{625}}$$
Step-by-Step Solution
Verified Answer
The result of the given expression is 3.
1Step 1: Solve the Inside of the Brackets
Firstly, calculate the square root of 16 and the square root of 625. For this, apply the concept of perfect squares (In maths, perfect squares are numbers that are squares of integers. For instance, squares of the integer 2 is 4 and this 4 is a perfect square.). The results are \( \sqrt[4]{16}=2 \) and \( \sqrt{625}=25 \).
2Step 2: Summing the Results
After finding the square roots of the given numbers, add them together. Thus, calculate \( 2+25=27 \)
3Step 3: Calculate the Cube Root
The last operation is to calculate the cube root of the result obtained in step 2. A cube root of a number is a value that, when cubed, gives the original number. The cube root of 27 is 3, so the output is \( \sqrt[3]{27}=3 \)
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Problem 108
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