Math / Numbers & Operations

Question妏, Simplify. $\sqrt{490}$

Studdy Solution

STEP 1

What is this asking? We need to simplify the square root of 490.
Basically, we want to find the nicest, cleanest way to write $\sqrt{490}$ . Watch out! Don't just grab a calculator!
We want to simplify this square root, not just get a decimal approximation.

STEP 2

1. Find factors
2. Simplify the root

STEP 3

Alright, let's break down that 490!
We're looking for perfect square factors, numbers we can easily take the square root of.
Think: 4, 9, 16, 25, 36, 49... Do any of those divide evenly into 490?

STEP 4

Hey, 49 jumps out! $490 = 49 \cdot 10$ .
That's awesome because 49 is a perfect square!

STEP 5

Now we can rewrite our expression: $\sqrt{490} = \sqrt{49 \cdot 10}$ Remember, the square root of a product is the product of the square roots!

STEP 6

So, we can separate the square roots: $\sqrt{49 \cdot 10} = \sqrt{49} \cdot \sqrt{10}$

STEP 7

We know that $\sqrt{49} = 7$ , so we have: $\sqrt{49} \cdot \sqrt{10} = 7 \cdot \sqrt{10}$

STEP 8

And that's it!
We can't simplify $\sqrt{10}$ any further, so our final simplified form is $7\sqrt{10}$ !

STEP 9

$7\sqrt{10}$

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Question妏, Simplify. $\sqrt{490}$

Studdy Solution

STEP 1

What is this asking? We need to simplify the square root of 490.
Basically, we want to find the nicest, cleanest way to write $\sqrt{490}$ . Watch out! Don't just grab a calculator!
We want to simplify this square root, not just get a decimal approximation.

STEP 2

1. Find factors
2. Simplify the root

STEP 3

Alright, let's break down that 490!
We're looking for perfect square factors, numbers we can easily take the square root of.
Think: 4, 9, 16, 25, 36, 49... Do any of those divide evenly into 490?

STEP 4

Hey, 49 jumps out! $490 = 49 \cdot 10$ .
That's awesome because 49 is a perfect square!

STEP 5

Now we can rewrite our expression: $\sqrt{490} = \sqrt{49 \cdot 10}$ Remember, the square root of a product is the product of the square roots!

STEP 6

So, we can separate the square roots: $\sqrt{49 \cdot 10} = \sqrt{49} \cdot \sqrt{10}$

STEP 7

We know that $\sqrt{49} = 7$ , so we have: $\sqrt{49} \cdot \sqrt{10} = 7 \cdot \sqrt{10}$

STEP 8

And that's it!
We can't simplify $\sqrt{10}$ any further, so our final simplified form is $7\sqrt{10}$ !

STEP 9

$7\sqrt{10}$

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Question妏, Simplify. 490\sqrt{490}490​

Studdy Solution

STEP 1

What is this asking? We need to simplify the square root of 490.Basically, we want to find the nicest, cleanest way to write 490 \sqrt{490} 490​. Watch out! Don't just grab a calculator!We want to simplify this square root, not just get a decimal approximation.

STEP 2

1. Find factors2. Simplify the root

STEP 3

Alright, let's **break down** that 490!We're looking for **perfect square factors**, numbers we can easily take the square root of.Think: 4, 9, 16, 25, 36, 49... Do any of those divide evenly into 490?

STEP 4

Hey, 49 jumps out! 490=49⋅10490 = 49 \cdot 10490=49⋅10.That's awesome because 49 is a **perfect square**!

STEP 5

Now we can rewrite our expression: 490=49⋅10 \sqrt{490} = \sqrt{49 \cdot 10} 490​=49⋅10​ Remember, the square root of a product is the product of the square roots!

STEP 6

So, we can **separate** the square roots: 49⋅10=49⋅10 \sqrt{49 \cdot 10} = \sqrt{49} \cdot \sqrt{10} 49⋅10​=49​⋅10​

STEP 7

We know that 49=7\sqrt{49} = 749​=7, so we have: 49⋅10=7⋅10 \sqrt{49} \cdot \sqrt{10} = 7 \cdot \sqrt{10} 49​⋅10​=7⋅10​

STEP 8

And that's it!We can't simplify 10\sqrt{10}10​ any further, so our **final simplified form** is 7107\sqrt{10}710​!

STEP 9

7107\sqrt{10}710​

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Question妏, Simplify. $\sqrt{490}$

What is this asking? We need to simplify the square root of 490.
Basically, we want to find the nicest, cleanest way to write $\sqrt{490}$ . Watch out! Don't just grab a calculator!
We want to simplify this square root, not just get a decimal approximation.

1. Find factors
2. Simplify the root

Alright, let's break down that 490!
We're looking for perfect square factors, numbers we can easily take the square root of.
Think: 4, 9, 16, 25, 36, 49... Do any of those divide evenly into 490?

Hey, 49 jumps out! $490 = 49 \cdot 10$ .
That's awesome because 49 is a perfect square!

Now we can rewrite our expression: $\sqrt{490} = \sqrt{49 \cdot 10}$ Remember, the square root of a product is the product of the square roots!

So, we can separate the square roots: $\sqrt{49 \cdot 10} = \sqrt{49} \cdot \sqrt{10}$

We know that $\sqrt{49} = 7$ , so we have: $\sqrt{49} \cdot \sqrt{10} = 7 \cdot \sqrt{10}$

And that's it!
We can't simplify $\sqrt{10}$ any further, so our final simplified form is $7\sqrt{10}$ !

$7\sqrt{10}$