Math / Numbers & Operations

QuestionSimplify the following. $\sqrt{300}$

Studdy Solution

STEP 1

What is this asking? We need to simplify the square root of 300, making it as small and neat as possible! Watch out! Don't forget to look for perfect squares hiding inside!

STEP 2

1. Find a perfect square factor.
2. Simplify the square root.

STEP 3

Alright, let's break down $\sqrt{300}$ !
We're on the hunt for perfect squares that are factors of 300.
Remember, a perfect square is a number that's the result of squaring an integer.
Think 4 (2 squared), 9 (3 squared), 16 (4 squared), 25 (5 squared), and so on.
We want to find the biggest perfect square that divides evenly into 300.

STEP 4

Let's think it through!
We can see that 100 is a factor of 300, and 100 is a perfect square (10 times 10 is 100)!
So, we can rewrite 300 as $100 \cdot 3$ .

STEP 5

Now, we can rewrite our square root: $\sqrt{300} = \sqrt{100 \cdot 3}$ .

STEP 6

Using the product property of square roots, which says $\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}$ , we can separate the square root into two parts: $\sqrt{100 \cdot 3} = \sqrt{100} \cdot \sqrt{3}$ .

STEP 7

Since the square root of 100 is 10, we simplify to $10 \cdot \sqrt{3}$ , or $10\sqrt{3}$ .
Boom!

STEP 8

Our simplified answer is $10\sqrt{3}$ !

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QuestionSimplify the following. $\sqrt{300}$

Studdy Solution

STEP 1

What is this asking? We need to simplify the square root of 300, making it as small and neat as possible! Watch out! Don't forget to look for perfect squares hiding inside!

STEP 2

1. Find a perfect square factor.
2. Simplify the square root.

STEP 3

STEP 4

Let's think it through!
We can see that 100 is a factor of 300, and 100 is a perfect square (10 times 10 is 100)!
So, we can rewrite 300 as $100 \cdot 3$ .

STEP 5

Now, we can rewrite our square root: $\sqrt{300} = \sqrt{100 \cdot 3}$ .

STEP 6

Using the product property of square roots, which says $\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}$ , we can separate the square root into two parts: $\sqrt{100 \cdot 3} = \sqrt{100} \cdot \sqrt{3}$ .

STEP 7

Since the square root of 100 is 10, we simplify to $10 \cdot \sqrt{3}$ , or $10\sqrt{3}$ .
Boom!

STEP 8

Our simplified answer is $10\sqrt{3}$ !

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QuestionSimplify the following. 300\sqrt{300}300​

Studdy Solution

STEP 1

What is this asking? We need to simplify the square root of 300, making it as small and neat as possible! Watch out! Don't forget to look for perfect squares hiding inside!

STEP 2

1. Find a perfect square factor.2. Simplify the square root.

STEP 3

STEP 4

Let's **think it through**!We can see that 100 is a factor of 300, and 100 is a perfect square (10 times 10 is 100)!So, we can rewrite 300 as 100⋅3100 \cdot 3100⋅3.

STEP 5

Now, we can **rewrite** our square root: 300=100⋅3\sqrt{300} = \sqrt{100 \cdot 3}300​=100⋅3​.

STEP 6

Using the **product property of square roots**, which says a⋅b=a⋅b\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}a⋅b​=a​⋅b​, we can **separate** the square root into two parts: 100⋅3=100⋅3\sqrt{100 \cdot 3} = \sqrt{100} \cdot \sqrt{3}100⋅3​=100​⋅3​.

STEP 7

Since the square root of 100 is 10, we **simplify** to 10⋅310 \cdot \sqrt{3}10⋅3​, or 10310\sqrt{3}103​.Boom!

STEP 8

Our simplified answer is 10310\sqrt{3}103​!

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Studdy solves anything!

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QuestionSimplify the following. $\sqrt{300}$

1. Find a perfect square factor.
2. Simplify the square root.

Let's think it through!
We can see that 100 is a factor of 300, and 100 is a perfect square (10 times 10 is 100)!
So, we can rewrite 300 as $100 \cdot 3$ .

Now, we can rewrite our square root: $\sqrt{300} = \sqrt{100 \cdot 3}$ .

Using the product property of square roots, which says $\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}$ , we can separate the square root into two parts: $\sqrt{100 \cdot 3} = \sqrt{100} \cdot \sqrt{3}$ .

Since the square root of 100 is 10, we simplify to $10 \cdot \sqrt{3}$ , or $10\sqrt{3}$ .
Boom!

Our simplified answer is $10\sqrt{3}$ !