Chapter 11: Q. 8.25 (page 1069)

Simplify $\sqrt{48}$ .

Short Answer

Expert verified

The value of the expression is $4 \sqrt{3}$ .

Step by step solution

Step 1. Given and explanation.

We have $\sqrt{48}$ .

Firstly, we will find the largest perfect square factor of the given number in the radicand.

Then using it, we will rewrite the expression as the product of two factors.

Then using the product rule, we will rewrite the radical as the product of two radicals. Simplifying the expression will give us value.

Step 2. Rewriting radical as a product of two radicals using a perfect square.

We have $\sqrt{48}$ .

We have $16$ as the largest perfect square factor of $48$ as $16 \times 3 = 48$ and
${(4)}^{2} = 16$ .

So we will rewrite the radical as product of two radicals using the product rule as,
$\sqrt{48} = \sqrt{16 \times 3} = \sqrt{16} \times \sqrt{3}$

Step 3. Simplifying the expression.

We have $\sqrt{16} \times \sqrt{3}$ .

We can write $\sqrt{16}$ as $4$ because $\sqrt{16} = \sqrt{4 \times 4}$ .

So using it, we get the value as

$= \sqrt{16} \times \sqrt{3} = 4 \sqrt{3}$

Thus the value of the expression is $4 \sqrt{3}$ .

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Simplify $\sqrt{48}$ .

Short Answer

Step by step solution

Step 1. Given and explanation.

Step 2. Rewriting radical as a product of two radicals using a perfect square.

Step 3. Simplifying the expression.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Discrete Mathematics

Logic and Functions

Mechanics Maths

Statistics

Calculus

Study anywhere. Anytime. Across all devices.

Simplify48.

Short Answer

Step by step solution

Step 1. Given and explanation.

Step 2. Rewriting radical as a product of two radicals using a perfect square.

Step 3. Simplifying the expression.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Discrete Mathematics

Logic and Functions

Mechanics Maths

Statistics

Calculus

Study anywhere. Anytime. Across all devices.

Simplify $\sqrt{48}$ .