Math Problem Statement

240\sqrt{40}

Solution

To simplify 40\sqrt{40}, we first factor the number under the square root:

40=4×10=22×1040 = 4 \times 10 = 2^2 \times 10

Now, take the square root:

40=4×10=4×10=210\sqrt{40} = \sqrt{4 \times 10} = \sqrt{4} \times \sqrt{10} = 2\sqrt{10}

So, the simplified form of 40\sqrt{40} is:

210\boxed{2\sqrt{10}}

Would you like more details on this, or do you have any questions?

Here are 5 related questions you might want to explore:

  1. What is the square root of 90 in its simplest radical form?
  2. How do you simplify 72\sqrt{72}?
  3. Can you explain how to factor a number under a square root?
  4. How do you simplify cube roots, like 543\sqrt[3]{54}?
  5. What are perfect squares, and how do they relate to simplifying square roots?

Tip: When simplifying square roots, look for the largest perfect square that is a factor of the number under the radical sign.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Simplifying Radicals
Square Roots

Formulas

\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}

Theorems

Properties of Square Roots

Suitable Grade Level

Grades 6-8