Question

√28+√63+√175
show work please

Answer 1

Can you factor 28 into two numbers, one of which is a perfect square?

Answer 2

7*4?

Answer 3

In this case, the perfect squares are the squares of the natural numbers, 1, 2, 3, 4, ..., so they are 1, 4, 9, 16, ...

Answer 4

Great.

Answer 5

Now can you do the same for 63?

Answer 6

7*9

Answer 7

Great again.
Now do the same for 175.

Answer 8

7*25 I THINK

Answer 9

Correct again.

This is what we have now:

\(\sqrt{28} + \sqrt{63} + \sqrt{175} \)

\(=\sqrt{4 \times 7} + \sqrt{9 \times 7} + \sqrt{25 \times 7} \)

Answer 10

what do I do after that

Answer 11

Split them up first:
\[(\sqrt{4}+\sqrt{7})+(\sqrt{7}+\sqrt{9})+(\sqrt{7}+\sqrt{25})\]
\[2\sqrt{7}+3\sqrt{7}+5\sqrt{7}\]
Add them up:
\[10\sqrt{7}\]

Answer 12

Now we separate the roots as follows:

\(=\sqrt{4}\sqrt{7} + \sqrt{9} \sqrt {7} + \sqrt{25} \sqrt{ 7} \)

Now take the square roots of all the perfect squares.

Answer 13

@PinkSapphire
You made a big mistake.

Answer 14

What?

Answer 15

\(=2\sqrt{7} + 3 \sqrt {7} + 5 \sqrt{ 7} \)

Now treat all terms as like terms, since they all have a factor of \(\sqrt{7} \) and add them up.

Answer 16

Compare your first line to my first line after yours.

Answer 17

It's basically the same...

Answer 18

where did the 2 befroe the √ come from?

Answer 19

No. Your idea is good, but your mistake is that the perfect squares you split up are MULTIPLIED by the remaining parts, not added.

Answer 20

No they are added...

Answer 21

I did say take the square roots of the perfect squares.
\(\sqrt{4} = 2\)

Answer 22

but that only equals 15.8745

Answer 23

Where did you get that from?

Answer 24

as I just typed the original equation in my calculator I got 26.4575

Answer 25

You can't do that...

Answer 26

I know thats why I'm asking for help

Answer 27

@Chrisgoblin Ignore this response. It's not correct.

@PinkSapphire Read below:

You wrote this (which is incorrect)

\( (\sqrt{4}+\sqrt{7})+(\sqrt{7}+\sqrt{9})+(\sqrt{7}+\sqrt{25})\)

If you continue correctly from it you'd get this:

\( =(2+\sqrt{7})+(\sqrt{7}+3)+(\sqrt{7}+5)\)

\( =2+ 3 + 5 + \sqrt{7}+\sqrt{7}+\sqrt{7}\)

\(= 10 + 3\sqrt 7\)

Which is not the same as the correct answer \(10 \sqrt{7} \)

Answer 28

OK, @Chrisgoblin
Let's continue.

Answer 29

@Chrisgoblin

Did you understand until this step?

\(=\sqrt{4}\sqrt{7} + \sqrt{9} \sqrt {7} + \sqrt{25} \sqrt{ 7}\)

Answer 30

yea

Answer 31

Here's how we continue. We take the square root of each perfect square. I color coded it to make it easier to see how you go form one step to the next.

\(=\color{red}{\sqrt{4}}\sqrt{7} + \color{green}{\sqrt{9}} \sqrt {7} + \color{blue}{\sqrt{25}} \sqrt{ 7}\)

\(=\color{red}{2}\sqrt{7} + \color{green}{3} \sqrt {7} + \color{blue}{5} \sqrt{ 7}\)

Answer 32

oh I see

Answer 33

Now the last step is to add all the square roots of 7 together.
Think of square root of 7 as x
Since 2x + 3x + 5x = 10x,
then similarly,
\(2\sqrt{7} + 3 \sqrt {7} + 5 \sqrt{ 7} = 10\sqrt{7}\)

Answer 34

26.4575

Answer 35

x=√7 right?

Answer 36

The answer \(10\sqrt 7\) is correct. If your problem is asking for an approximation, then you can use 26.4575, but my answer is exact.
Also, if an approximation were what the problem wants, you could just take the square root of each number in the beginning and added them all up. There isn't much work to show then.

Answer 37

Yes, \(x = \sqrt 7\)

Answer 38

thanks and do you think you could help me with one more problem @mathstudent55

Answer 39

You're welcome, and yes.

Answer 40

(√2w+5)+4=√25

Answer 41

The first one or the second one? (The difference is whetehr or not the w is also in the square root.)

\((\sqrt{2}w + 5) + 4 = \sqrt{25} \)

\((\sqrt{2w} + 5) + 4 = \sqrt{25} \)

Answer 42

its the square root of 2w +5 the top line covers 2w+5

Answer 43

thats why I put the parenthesis

Answer 44

Oh, ok. Let me write that, then.

Answer 45

You meant the parentheses after the root symbol.

√(2w+5)+4=√25

\(\sqrt{2w + 5} + 4 = \sqrt{25} \)

This is it now?

Answer 46

oh yea woops thats it

Answer 47

Ok. Let's solve it then.

Answer 48

First, take the square root of 25 on the right side.

Answer 49

\(\sqrt{2w + 5} + 4 = \color{red}{\sqrt{25}}\)

\(\sqrt{2w + 5} + 4 = \color{red}{5}\)

Answer 50

ok

Answer 51

Now subtract 4 from both sides. What do you get?

Answer 52

√(2w+5)=1

Answer 53

Good.
Now square both sides.

Answer 54

When you square a square root, just remove the square root symbol.

Answer 55

ok 2w+5=1

Answer 56

Great.
Now just solve for w.
Subtract 5 from both sides.
Then divide both sides by 2.

Answer 57

2w=-4

Answer 58

Now divide both sides by 2.

Answer 59

1w-2

Answer 60

w = -2

Answer 61

wow I feel stupid

Answer 62

*w=-2
so √(2*-2+5)+4=√25

Answer 63

so 5

Answer 64

There is one more check.
Sometimes when both sides of an equation are squared, extra solutions are introduced that are not solutions to the original equations. These extra solutions are called "extraneous solutions."

We need to check our solution in our original equation.

\(\sqrt{2w + 5} + 4 = \sqrt{25}\)

\(\sqrt{2(-2) + 5} + 4 = 5\)

\(\sqrt{-4 + 5} + 4 = 5\)

\(\sqrt{1} + 4 = 5\)

\(1 + 4 = 5\)

\(5 = 5\)

The solution is correct, w = -2.

Answer 65

thanks