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Nataly_w [17]
2 years ago
8

Simplify sqrt(3 + 2 sqrt 2) ...?

Mathematics
2 answers:
trasher [3.6K]2 years ago
8 0
The answer is 1 + √2

sqrt(2) is \sqrt{2}
sqrt(3 + 2 sqrt 2) is \sqrt{3 +2 \sqrt{2} }
Now, let's simplify \sqrt{3 +2 \sqrt{2} }.
We will use square of sum: (a + b)² = a² + 2ab + b²

\sqrt{3 +2 \sqrt{2} } = \sqrt{1+2+2 \sqrt{2} }= \sqrt{1+2 \sqrt{2}+2 }= \\ 
= \sqrt{1^{2} +2*1* \sqrt{2} + (\sqrt{2} ) ^{2} } = \sqrt{(1+ \sqrt{2}) ^{2}} =1+ \sqrt{2}
seropon [69]2 years ago
6 0

Answer:

1+\sqrt{2}

Step-by-step explanation:

We have been given a radical expression \sqrt{3+2\sqrt{2}}. We are asked to simplify the given expression.

We will add (\sqrt{2})^2-2 to our given expression as after adding and subtracting same quantity the value of our expression will be same.

\sqrt{3+2\sqrt{2}+(\sqrt{2})^2-2}

\sqrt{3-2+2\sqrt{2}+(\sqrt{2})^2}

\sqrt{1+2\sqrt{2}+(\sqrt{2})^2}

Using perfect square formula (a+b)^2=a^2+2ab+b^2 we can rewrite our expression as:

\sqrt{1^2+2\sqrt{2}\cdot 1+(\sqrt{2})^2}

\sqrt{(1+\sqrt{2})^2}

Applying radical rule \sqrt[n]{x^n} =x, we will get,

(1+\sqrt{2})^{\frac{2}{2}}=1+\sqrt{2}

Therefore, the simplified form of our given expression would be 1+\sqrt{2}.

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ANEK [815]

Situation :  Earnings of 15 dollars is represented as integer as +15 .

<u>Step-by-step explanation:</u>

Here we have , to Write an integer to represent the following situation: Earnings of 15 dollars  . Let's find out:

Integer : An integer in math is composes of both positive and negative whole number as : -3,-2,-1,0,1,2,3 etc ..........

According to statement , we need to write an integer to represent the statement : EARNINGS OF 15 DOLLARS  . There is word earnings in statement that means increment or increase , and other words are 15 dollars or $15 . So , above statement means increase of 15 dollars which can be represented as an integer as given below :

⇒ +15

Where + sign means increase or , with reference to statement it refers to word earnings . Therefore , Situation :  Earnings of 15 dollars is represented as integer as +15 .

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2 years ago
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SVETLANKA909090 [29]

Answer:

y = -3x - 1

Step-by-step explanation:

The slope intercept form of the equation of a line is:

y = mx + b

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First, we find the slope of the line using the two given points.

m = slope = (y2 - y1)/(x2 - x1) = (2 - (-7))/(-1 - 2) = (2 + 7)/(-3) = 9/(-3) = -3

Now we plug in the slope we found into the equation above.

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We need to find the value of b, the y-intercept. We use the coordinates of one of the given points for x and y, and we solve for b. Let's use point (2, -7), so x = 2, and y = -7.

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42
let the smallest even number be x, than the four even numbers are x, x+2, x+4, x+6, their sum is 180

x+x+2+x+4+x+6=180
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3 years ago
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Answer:

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Step-by-step explanation:

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