Math Problem Statement

Complete the square root and cube root equations: 9a: √(□) = 18, 9b: √(□) = 20, 10a: ³√(□) = 7, 10b: ³√(□) = 9.

Solution

Let’s solve the questions one by one:

Question 9

You are asked to complete the square root equations:

Part a: =18\sqrt{\Box} = 18

To solve, square both sides: =182=324\Box = 18^2 = 324 Answer: =324\Box = 324.

Part b: =20\sqrt{\Box} = 20

Square both sides: =202=400\Box = 20^2 = 400 Answer: =400\Box = 400.


Question 10

You are asked to complete the cube root equations:

Part a: 3=7\sqrt[3]{\Box} = 7

To solve, cube both sides: =73=343\Box = 7^3 = 343 Answer: =343\Box = 343.

Part b: 3=9\sqrt[3]{\Box} = 9

Cube both sides: =93=729\Box = 9^3 = 729 Answer: =729\Box = 729.


Final Answers:

  • 9a: =324\Box = 324
  • 9b: =400\Box = 400
  • 10a: =343\Box = 343
  • 10b: =729\Box = 729

Would you like to review any step in more detail?


Related Questions:

  1. What is the square root of 144?
  2. Solve for xx in x2=625x^2 = 625.
  3. What is the cube of 5?
  4. Simplify 5123\sqrt[3]{512}.
  5. Can you express 643\sqrt[3]{64} in exponential form?

Tip:

To check your square or cube root calculations, always reverse the operation by squaring or cubing the result.

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Math Problem Analysis

Mathematical Concepts

Square Roots
Cube Roots
Exponents

Formulas

If √(x) = y, then x = y²
If ³√(x) = y, then x = y³

Theorems

Properties of Exponents

Suitable Grade Level

Grades 6-8