Solved on Jan 20, 2024

Simplify the expression $9 \sqrt{5} + \sqrt{45}$ .

STEP 1

Assumptions
1. We are asked to simplify the expression $9 \sqrt{5}+\sqrt{45}$ .
2. To simplify the expression, we will need to simplify any radical terms and combine like terms if possible.

STEP 2

First, we need to identify any radical terms that can be simplified. The term $\sqrt{45}$ can be simplified because 45 has a square factor.
$\sqrt{45} = \sqrt{9 \times 5}$

STEP 3

Since the square root of a product is equal to the product of the square roots of the factors, we can simplify $\sqrt{45}$ by taking the square root of 9 out of the radical.
$\sqrt{45} = \sqrt{9} \times \sqrt{5}$

STEP 4

Calculate the square root of 9, which is a perfect square.
$\sqrt{9} = 3$

STEP 5

Now, we can rewrite $\sqrt{45}$ as $3\sqrt{5}$ .
$\sqrt{45} = 3\sqrt{5}$

STEP 6

We now have the original expression with $\sqrt{45}$ simplified.
$9 \sqrt{5} + \sqrt{45} = 9 \sqrt{5} + 3\sqrt{5}$

STEP 7

Since $9 \sqrt{5}$ and $3\sqrt{5}$ are like terms (they both have the radical $\sqrt{5}$ ), we can combine them by adding their coefficients.
$9 \sqrt{5} + 3\sqrt{5} = (9 + 3)\sqrt{5}$

STEP 8

Add the coefficients.
$9 + 3 = 12$

STEP 9

Finally, write down the simplified expression.
$9 \sqrt{5} + 3\sqrt{5} = 12\sqrt{5}$
The expression $9 \sqrt{5}+\sqrt{45}$ simplifies to $12\sqrt{5}$ .

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Simplify the expression $9 \sqrt{5} + \sqrt{45}$ .

STEP 1

Assumptions
1. We are asked to simplify the expression $9 \sqrt{5}+\sqrt{45}$ .
2. To simplify the expression, we will need to simplify any radical terms and combine like terms if possible.

STEP 2

First, we need to identify any radical terms that can be simplified. The term $\sqrt{45}$ can be simplified because 45 has a square factor.
$\sqrt{45} = \sqrt{9 \times 5}$

STEP 3

Since the square root of a product is equal to the product of the square roots of the factors, we can simplify $\sqrt{45}$ by taking the square root of 9 out of the radical.
$\sqrt{45} = \sqrt{9} \times \sqrt{5}$

STEP 4

Calculate the square root of 9, which is a perfect square.
$\sqrt{9} = 3$

STEP 5

Now, we can rewrite $\sqrt{45}$ as $3\sqrt{5}$ .
$\sqrt{45} = 3\sqrt{5}$

STEP 6

We now have the original expression with $\sqrt{45}$ simplified.
$9 \sqrt{5} + \sqrt{45} = 9 \sqrt{5} + 3\sqrt{5}$

STEP 7

Since $9 \sqrt{5}$ and $3\sqrt{5}$ are like terms (they both have the radical $\sqrt{5}$ ), we can combine them by adding their coefficients.
$9 \sqrt{5} + 3\sqrt{5} = (9 + 3)\sqrt{5}$

STEP 8

Add the coefficients.
$9 + 3 = 12$

STEP 9

Finally, write down the simplified expression.
$9 \sqrt{5} + 3\sqrt{5} = 12\sqrt{5}$
The expression $9 \sqrt{5}+\sqrt{45}$ simplifies to $12\sqrt{5}$ .

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Simplify the expression 95+459 \sqrt{5} + \sqrt{45}95​+45​.

STEP 1

Assumptions1. We are asked to simplify the expression 95+459 \sqrt{5}+\sqrt{45}95​+45​.2. To simplify the expression, we will need to simplify any radical terms and combine like terms if possible.

STEP 2

First, we need to identify any radical terms that can be simplified. The term 45\sqrt{45}45​ can be simplified because 45 has a square factor.45=9×5\sqrt{45} = \sqrt{9 \times 5}45​=9×5​

STEP 3

Since the square root of a product is equal to the product of the square roots of the factors, we can simplify 45\sqrt{45}45​ by taking the square root of 9 out of the radical.45=9×5\sqrt{45} = \sqrt{9} \times \sqrt{5}45​=9​×5​

STEP 4

Calculate the square root of 9, which is a perfect square.9=3\sqrt{9} = 39​=3

STEP 5

Now, we can rewrite 45\sqrt{45}45​ as 353\sqrt{5}35​.45=35\sqrt{45} = 3\sqrt{5}45​=35​

STEP 6

We now have the original expression with 45\sqrt{45}45​ simplified.95+45=95+359 \sqrt{5} + \sqrt{45} = 9 \sqrt{5} + 3\sqrt{5}95​+45​=95​+35​

STEP 7

Since 959 \sqrt{5}95​ and 353\sqrt{5}35​ are like terms (they both have the radical 5\sqrt{5}5​), we can combine them by adding their coefficients.95+35=(9+3)59 \sqrt{5} + 3\sqrt{5} = (9 + 3)\sqrt{5}95​+35​=(9+3)5​

STEP 8

Add the coefficients.9+3=129 + 3 = 129+3=12

STEP 9

Finally, write down the simplified expression.95+35=1259 \sqrt{5} + 3\sqrt{5} = 12\sqrt{5}95​+35​=125​The expression 95+459 \sqrt{5}+\sqrt{45}95​+45​ simplifies to 12512\sqrt{5}125​.

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Simplify the expression $9 \sqrt{5} + \sqrt{45}$ .

Assumptions
1. We are asked to simplify the expression $9 \sqrt{5}+\sqrt{45}$ .
2. To simplify the expression, we will need to simplify any radical terms and combine like terms if possible.

First, we need to identify any radical terms that can be simplified. The term $\sqrt{45}$ can be simplified because 45 has a square factor.
$\sqrt{45} = \sqrt{9 \times 5}$

Since the square root of a product is equal to the product of the square roots of the factors, we can simplify $\sqrt{45}$ by taking the square root of 9 out of the radical.
$\sqrt{45} = \sqrt{9} \times \sqrt{5}$

Calculate the square root of 9, which is a perfect square.
$\sqrt{9} = 3$

Now, we can rewrite $\sqrt{45}$ as $3\sqrt{5}$ .
$\sqrt{45} = 3\sqrt{5}$

We now have the original expression with $\sqrt{45}$ simplified.
$9 \sqrt{5} + \sqrt{45} = 9 \sqrt{5} + 3\sqrt{5}$

Since $9 \sqrt{5}$ and $3\sqrt{5}$ are like terms (they both have the radical $\sqrt{5}$ ), we can combine them by adding their coefficients.
$9 \sqrt{5} + 3\sqrt{5} = (9 + 3)\sqrt{5}$

Add the coefficients.
$9 + 3 = 12$

Finally, write down the simplified expression.
$9 \sqrt{5} + 3\sqrt{5} = 12\sqrt{5}$
The expression $9 \sqrt{5}+\sqrt{45}$ simplifies to $12\sqrt{5}$ .