Math Problem Statement

Simplify the radical expression. 5 32x10 Write your answer in the form A, 5 B, or A5 B, where A and B are constants or expressions in x. Use at most one radical in your answer, and at most one absolute value symbol in your expression for A.

Solution

It seems like you want to simplify a radical expression, but the provided expression isn't fully clear. Based on the format "5 32x10" you've mentioned, I think you may have meant to simplify something like:

53210x\sqrt{5 \cdot 32 \cdot 10 \cdot x}

However, it could also be a different expression, so please confirm or clarify if that’s what you meant. Assuming it is, here's how you would simplify it:

Step 1: Simplify the product inside the square root

First, multiply the constants and variables:

532=1605 \cdot 32 = 160 16010=1600160 \cdot 10 = 1600

So the expression inside the square root is:

1600x\sqrt{1600x}

Step 2: Simplify the square root

We now simplify the square root of 1600x1600x.

The square root of 16001600 is 4040, so:

1600x=1600x=40x\sqrt{1600x} = \sqrt{1600} \cdot \sqrt{x} = 40\sqrt{x}

Thus, the simplified expression is:

40x40\sqrt{x}

This is the simplest form with only one radical.

If you had a different expression in mind, let me know! Would you like me to go over more details or further clarify anything?


Related Questions:

  1. How do you simplify square roots of larger expressions?
  2. What are the rules for simplifying square roots with variables?
  3. What happens if the expression inside the radical is a perfect square?
  4. How do you handle negative values inside square roots in real numbers?
  5. How can we handle square roots of expressions involving absolute values?

Tip: Always try to factor the number inside the square root to separate out any perfect squares, as it simplifies the process.

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Math Problem Analysis

Mathematical Concepts

Radical Expressions
Square Roots
Simplification of Radicals

Formulas

sqrt(a * b) = sqrt(a) * sqrt(b)

Theorems

Simplification of square roots
Handling of constants and variables inside square roots

Suitable Grade Level

Grades 8-10