Math / Numbers & Operations

Question $\sqrt{348}$

Studdy Solution

STEP 1

1. We are tasked with simplifying the square root of $348$ .
2. We will express the square root in its simplest radical form.

STEP 2

1. Factor the number under the square root.
2. Identify and extract perfect squares.
3. Simplify the expression.

STEP 3

Factor $348$ into its prime factors.
First, divide by $2$ (since $348$ is even):
$348 \div 2 = 174$
Divide $174$ by $2$ again (since $174$ is even):
$174 \div 2 = 87$
Now, $87$ is not divisible by $2$ , so try dividing by $3$ :
$87 \div 3 = 29$
Since $29$ is a prime number, the prime factorization of $348$ is:
$348 = 2^2 \times 3 \times 29$

STEP 4

Identify and extract perfect squares from the factorization.
The perfect square in the factorization is $2^2$ .

STEP 5

Simplify the square root by extracting the perfect square:
$\sqrt{348} = \sqrt{2^2 \times 3 \times 29}$
Extract $2^2$ from the square root:
$\sqrt{348} = 2 \times \sqrt{3 \times 29}$
The simplified form of $\sqrt{348}$ is:
$\boxed{2\sqrt{87}}$

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms