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Chapter 0: Problem 109

Evaluate each expression. $$\sqrt[3]{\sqrt[4]{16}+\sqrt{625}}$$

Short Answer

Expert verified
The result of the given expression is 3.

Step by step solution

01

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 \( \sqrt{625}=25 \).
02

Summing the Results

After finding the square roots of the given numbers, add them together. Thus, calculate \( 2+25=27 \)
03

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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Most popular questions from this chapter

Explain how to convert from decimal to scientific notation and give an example.

Suppose that a polynomial contains four terms. Explain how to use factoring by grouping to factor the polynomial.

Putting Numbers into Perspective. A large number can be put into perspective by comparing it with another number. For example, we put the \(\$ 15.2\) trillion national debt (Example 12 ) and the \(\$ 2.17\) trillion the government collected in taxes (Exercise 115 ) by comparing these numbers to the number of U.S. citizens. For this project, each group member should consult an almanac, a newspaper, or the Internet to find a number greater than one million. Explain to other members of the group the context in which the large number is used. Express the number in scientific notation. Then put the number into perspective by comparing it with another number.

Evaluate each expression without using a calculator. $$27^{\frac{1}{3}}$$

Exercises \(142-144\) will help you prepare for the material covered in the next section. Multiply: \(\quad\left(2 x^{3} y^{2}\right)\left(5 x^{4} y^{7}\right)\)
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