Math Problem Statement

awnser it

Mona has a cat that weighs 3.9 kilograms. Noura has a cat that weighs the cube root of 68 kilograms. Sara has a cat that weighs the square root of 30 kilograms. Which girl has the lightest cat?

Solution

Let's break down the problem step by step:

  • Mona has a cat that weighs 3.9 kilograms.
  • Noura has a cat that weighs 683\sqrt[3]{68} kilograms (the cube root of 68).
  • Sara has a cat that weighs 30\sqrt{30} kilograms (the square root of 30).

Now, we will calculate the actual weights for Noura's and Sara's cats:

  1. Noura's cat: 6834.1kilograms\sqrt[3]{68} \approx 4.1 \, \text{kilograms}

  2. Sara's cat: 305.48kilograms\sqrt{30} \approx 5.48 \, \text{kilograms}

The weights are:

  • Mona's cat: 3.9 kg
  • Noura's cat: 4.1 kg
  • Sara's cat: 5.48 kg

Clearly, Mona's cat weighs the least at 3.9 kilograms.

The correct answer is Mona.

Do you want further details or have any other questions?

Here are 5 related questions:

  1. How do you calculate cube roots manually?
  2. What is the difference between a square root and a cube root?
  3. How can we estimate roots of non-perfect cubes or squares without a calculator?
  4. In what scenarios do cube roots frequently appear in real-life applications?
  5. Why is it important to compare roots in mathematics?

Tip: Roots can often be estimated using approximation methods if calculators are unavailable!

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Math Problem Analysis

Mathematical Concepts

Cube Roots
Square Roots
Comparison of Numbers

Formulas

Cube root of x: ∛x
Square root of x: √x

Theorems

Properties of Cube Roots
Properties of Square Roots

Suitable Grade Level

Grades 6-8