Simplify 5√2 x √8 / 2√2

[Tserro]

Hi all,
I’m looking to refresh my brain for helping my children in their Nat 5’s
i have an equation which is telling me I’m wrong

Simplify 5√2 x √8 / 2√2

i worked it out as

= 5√16 / 2√2
= 20 / 2√2
= 10√2

where am I going wrong?

 

[Tserro]

So sorry.
I’ve since worked it out

5√2 x √8 / 2√2
= 5√2 x √2x4 / 2√2
= 5√2 x 2√2 / 2√2
= 5√2

 

[stapel]

Hi all,
I’m looking to refresh my brain for helping my children in their Nat 5’s
i have an equation which is telling me I’m wrong

Simplify 5√2 x √8 / 2√2

i worked it out as

= 5√16 / 2√2
= 20 / 2√2
= 10√2

where am I going wrong?

In going from the second line to the last line, you somehow moved the [imath]\sqrt{2\;}[/imath] from the denominator to the numerator. If you leave the radical in the denominator and then rationalize the denominator, then you'll get the correct value.

 

[blamocur]

So sorry.
I’ve since worked it out

5√2 x √8 / 2√2
= 5√2 x √2x4 / 2√2
= 5√2 x 2√2 / 2√2
= 5√2

Nothing to be sorry about. Making mistakes and fixing them -- whether on your own or with help from others -- is, IMHO, the most effective way to learn.

 

[Steven G]

Hi all,
I’m looking to refresh my brain for helping my children in their Nat 5’s
i have an equation which is telling me I’m wrong

Simplify 5√2 x √8 / 2√2

What you wrote is \(\displaystyle \dfrac{5\sqrt{2}x\sqrt{8}}{2}\sqrt{2}\ =\ \dfrac{5\sqrt{2}x\sqrt{8}\sqrt{2}}{2}\) but you seem to be solving for \(\displaystyle \dfrac{5\sqrt{2}x\sqrt{8}}{2\sqrt{2}}\)

Please not that 5*4/2*8\(\displaystyle \neq\)20/16. Rather it equals 80. If you want to divide by 2*8 you need to put parentheses. Like 5*4/(2*8)=20/16

 

[Dr.Peterson]

What you wrote is \(\displaystyle \dfrac{5\sqrt{2}\times\sqrt{8}}{2}\sqrt{2}\ =\ \dfrac{5\sqrt{2}\times\sqrt{8}\sqrt{2}}{2}\) but you seem to be solving for \(\displaystyle \dfrac{5\sqrt{2}\times\sqrt{8}}{2\sqrt{2}}\)

Please not[e] that 5*4/2*8\(\displaystyle \neq\)20/16. Rather it equals 80. If you want to divide by 2*8 you need to put parentheses. Like 5*4/(2*8)=20/16

This is true; but the equivalent without the multiplication signs, as in "5√2 x √8 / 2√2", is not interpreted that way everywhere. It appears to be taught in some places (perhaps largely outside the U.S.) that in an expression like the one given, the multiplication is taken as being in the denominator. Clearly the OP takes it that way; whether it is what is taught there is unclear, but quite possible.

Because of this variation, it is recommended to use parentheses, or, preferably, the fraction form, for clarity.