Math / Numbers & Operations

QuestionSimplify. $(\sqrt{5})^{2}$

Studdy Solution

STEP 1

What is this asking? We're asked to find the value of the square root of 5, squared. Watch out! Remember squaring something and taking the square root of something are inverse operations!
They undo each other.

STEP 2

1. Simplify the expression

STEP 3

Alright, let's tackle this problem!
We have $(\sqrt{5})^2$ .
Remember, the square root of a number is a value that, when multiplied by itself, gives us the original number.

STEP 4

So, $\sqrt{5}$ is the number that, when multiplied by itself, gives us 5.
Let's write that out: $\sqrt{5} \cdot \sqrt{5} = 5$ .

STEP 5

Now, look back at our original expression: $(\sqrt{5})^2$ .
This is the same as $\sqrt{5}$ multiplied by itself.
That is, $(\sqrt{5})^2 = \sqrt{5} \cdot \sqrt{5}$ .

STEP 6

But we just saw that $\sqrt{5} \cdot \sqrt{5} = 5$ !
So, $(\sqrt{5})^2 = 5$ .
Boom!

STEP 7

$(\sqrt{5})^2 = 5$

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QuestionSimplify. $(\sqrt{5})^{2}$

Studdy Solution

STEP 1

What is this asking? We're asked to find the value of the square root of 5, squared. Watch out! Remember squaring something and taking the square root of something are inverse operations!
They undo each other.

STEP 2

1. Simplify the expression

STEP 3

Alright, let's tackle this problem!
We have $(\sqrt{5})^2$ .
Remember, the square root of a number is a value that, when multiplied by itself, gives us the original number.

STEP 4

So, $\sqrt{5}$ is the number that, when multiplied by itself, gives us 5.
Let's write that out: $\sqrt{5} \cdot \sqrt{5} = 5$ .

STEP 5

Now, look back at our original expression: $(\sqrt{5})^2$ .
This is the same as $\sqrt{5}$ multiplied by itself.
That is, $(\sqrt{5})^2 = \sqrt{5} \cdot \sqrt{5}$ .

STEP 6

But we just saw that $\sqrt{5} \cdot \sqrt{5} = 5$ !
So, $(\sqrt{5})^2 = 5$ .
Boom!

STEP 7

$(\sqrt{5})^2 = 5$

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QuestionSimplify. (5)2(\sqrt{5})^{2}(5​)2

Studdy Solution

STEP 1

What is this asking? We're asked to find the value of the square root of 5, squared. Watch out! Remember squaring something and taking the square root of something are *inverse operations*!They undo each other.

STEP 2

1. Simplify the expression

STEP 3

Alright, let's **tackle** this problem!We have (5)2(\sqrt{5})^2(5​)2.Remember, the square root of a number is a value that, when multiplied by itself, gives us the original number.

STEP 4

So, 5\sqrt{5}5​ is the number that, when multiplied by itself, gives us **5**.Let's write that out: 5⋅5=5\sqrt{5} \cdot \sqrt{5} = 55​⋅5​=5.

STEP 5

Now, look back at our original expression: (5)2(\sqrt{5})^2(5​)2.This is the same as 5\sqrt{5}5​ multiplied by itself.That is, (5)2=5⋅5(\sqrt{5})^2 = \sqrt{5} \cdot \sqrt{5}(5​)2=5​⋅5​.

STEP 6

But we just saw that 5⋅5=5\sqrt{5} \cdot \sqrt{5} = 55​⋅5​=5!So, (5)2=5(\sqrt{5})^2 = 5(5​)2=5.Boom!

STEP 7

(5)2=5(\sqrt{5})^2 = 5(5​)2=5

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QuestionSimplify. $(\sqrt{5})^{2}$

What is this asking? We're asked to find the value of the square root of 5, squared. Watch out! Remember squaring something and taking the square root of something are inverse operations!
They undo each other.

Alright, let's tackle this problem!
We have $(\sqrt{5})^2$ .
Remember, the square root of a number is a value that, when multiplied by itself, gives us the original number.

So, $\sqrt{5}$ is the number that, when multiplied by itself, gives us 5.
Let's write that out: $\sqrt{5} \cdot \sqrt{5} = 5$ .

Now, look back at our original expression: $(\sqrt{5})^2$ .
This is the same as $\sqrt{5}$ multiplied by itself.
That is, $(\sqrt{5})^2 = \sqrt{5} \cdot \sqrt{5}$ .

But we just saw that $\sqrt{5} \cdot \sqrt{5} = 5$ !
So, $(\sqrt{5})^2 = 5$ .
Boom!

$(\sqrt{5})^2 = 5$