Question

Operations with Radical Expressions
Simplify √44 - √11

Answer 1

ok - first notice that 11 is a prime number so \(\sqrt{11}\) is in its simplest form.

however, 44 is not a prime number - can you find its factors?

Answer 2

1, 2, 4, 11, 22, 44

Answer 3

ok, so we can write 44 as 4 * 11

Answer 4

next, do you know that:\[\sqrt{ab}=\sqrt{a}\times\sqrt{b}\]

Answer 5

yes

Answer 6

good, so we can write:\[\sqrt{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=?\]

Answer 7

Notice how the first radical can be written as a multiple of 11.\[\sqrt{44}-\sqrt{11}=\sqrt{11*4}-\sqrt{11}\]What I am about to do now is use the following rule:\[\sqrt{a*b}=\sqrt{a}\sqrt{b}\]Using this, let's re-write the radicals again:\[\sqrt{11*4}-\sqrt{11}=\sqrt{4}\sqrt{11}-\sqrt{11}=..?\]Can you take it on from here and evaluate the answe?

@LemonLeaf

Answer 8

@LemonLeaf you should be able to work out \(\sqrt{4}\)

Answer 9

ok, i think i get it now, thank you!! :)

Answer 10

yw :)