Question

what is the exact value of the equation
sqrt of 52 - a sqrt 12 + sqrt of 117

Answer 1

\[\sqrt{52} - \sqrt{13} + \sqrt{117}\]

Answer 2

\[\sqrt[4]{13}\]
\[\sqrt{13}\]
\[\sqrt[2]{39}\]
\[\sqrt[8]{39}\]

Answer 3

Notice that:

52 = 13 * 4
13 = 13 * 1
117 = 13 * 9

Answer 4

yes

Answer 5

And if I am right, the options should be:

(1) \(\large{4\sqrt{13}}\)
(2) \(\large{\sqrt{13}}\)
(3) \(\large{2\sqrt{13}}\)
(4) \(\large{8\sqrt{13}}\)

Answer 6

the options are above

Answer 7

Now, see:

\[\large{\sqrt{117} = \sqrt{13 * 9} = \sqrt{13} * \sqrt{9} = \sqrt{13} * 3}\]

Any doubt ?

Answer 8

no doubt

Answer 9

Good...

Similarly, can you write \(\large{\sqrt{52}}\) as \(\large{2*\sqrt{13}}\) ?

Remember that 52 = 13 * 4

Answer 10

ok

Answer 11

Great, so you have:

\[\sqrt{52} - \sqrt{13} + \sqrt{117}\]
\[= 2\sqrt{13} - \sqrt{13} + 3\sqrt{13}\]

Now can you solve this?

Answer 12

@SuperMcMadrid5 - Note the the expression in your question is not an equation because it contains no equal sign

Answer 13

it does not come with one

Answer 14

@SuperMcMadrid5 do you have some doubt ?

Answer 15

no, i cant solve it though

Answer 16

Its okay lets see:

\[= 2\sqrt{13} - \sqrt{13} + 3\sqrt{13}\]

Did you get until this ?

Answer 17

ok

Answer 18

Great!

So, now:

\[2\sqrt{13} - \sqrt{13} + 3\sqrt{13}\]

\[=\sqrt{13}(2-1+3)\]

Clear ?

Answer 19

clear

Answer 20

Superb !! :)

Now, what is the value of (2-1+3) ?

Answer 21

4

Answer 22

Great going!! Now one final thing:

\[=\sqrt{13}(2-1+3)\]

\[= 4\sqrt{13}\]

Now which option is this ?

Answer 23

its A

Answer 24

Thank you

Answer 25

Your welcome :)