Question

can anybody please help me with this?

Answer 1

you should do this:
factor each number inside the square roots into their "prime factors"

distribute the \( \sqrt{13}\) (multiply it times each term inside the parens)

use the rule
\[ \sqrt{a}\cdot \sqrt{b} = \sqrt{a\cdot b} \]
but don't actually multiply the numbers, just combine them inside one square root

now look for pairs to pull out of the square root.

Answer 2

\[6\sqrt{2} \times \sqrt{13} \times \sqrt{2}\]

Answer 3

@phi I distributed and got this. Is this correct?

Answer 4

when you distribute, you have to keep the plus sign
between the two terms

Answer 5

this is a multi - step problem

\[ \left(\sqrt{72} + \sqrt{26} \right)\sqrt{13}\]

distribute means multiply the sqrt(13) times each term inside the parens
Just write \(\sqrt{13}\) next to each term inside the parens.
can you do that ?

Answer 6

\[\sqrt {13} (\sqrt{72}) + \sqrt {13} (\sqrt {26})\] like this?

Answer 7

yes
next we use this rule on both terms
\[ \sqrt{a}\sqrt{b}= \sqrt{a\cdot b}\]
all that means is change
\( \sqrt{13} \sqrt{72} \) into \(\sqrt{13\cdot 72} \)
do that for both terms.

can you do that ?

Answer 8

\[\sqrt {13 \times 72} + \sqrt {13 \times 16}\]

Answer 9

like this?

Answer 10

you mean 26 not 16 in the 2nd term, right ?

Answer 11

yes sorry 26*

Answer 12

now factor the 72, because we want to find pairs
can you do that ?

Answer 13

\[6 \times \sqrt {2}\]

Answer 14

right?

Answer 15

for the first term, you start with
\[ \sqrt{13 \cdot 72 }\]
if we factor 72 into 2*36 = 2*6*6 we have
\[ \sqrt{13 \cdot 2\cdot 6 \cdot 6 }\]
now pull out the pair of 6's
what do you get ?

Answer 16

\[\sqrt {13 \times 2}\]

Answer 17

right?

Answer 18

yes, but with a 6 out front... (the pair of 6's come out of the radical, and one of the 6's goes in front.

try again

Answer 19

\[6 \sqrt {13 \times 2}\]

Answer 20

yes.
and now can you simplify the 2nd term
\[ \sqrt{13\cdot 26} \]

Answer 21

factor the 26 into 2*13
\[ \sqrt{13 \cdot 2 \cdot 13} \]
now pull out a pair (and put one of them out front )

Answer 22

\[13 \sqrt {2}\]

Answer 23

so now you have
\[ 6 \sqrt{13 \cdot 2 } + 13 \sqrt{2} \]
you can not do any more with this except multiply the 13*2 inside the radical
\[ 6 \sqrt{26 } + 13 \sqrt{2} \]
that is the answer

Answer 24

thank you SO MUCH!