1. Surd and Algebra Questions

Hi I am in year 10 and in the highest math class. We just started revising on surds and I have not been able to answer these two questions. The questions that I am stuck on are 3e and 3i. Sorry about the mirrored writing. Any help will be appreciated.

2. Re: Surd and Algebra Questions

\displaystyle \begin{align*} \sqrt{ 338 a^3 b^3 } &= \sqrt{ 2ab \cdot 169 a^2 b^2 } \\ &= \sqrt{2ab} \cdot \sqrt{ 169 } \cdot \sqrt{a^2} \cdot \sqrt{b^2} \\ &= 13|a||b| \, \sqrt{ 2ab } \end{align*}

See if you can follow a similar process with the others.

3. Re: Surd and Algebra Questions

Thankyou but can you please tell me how to do 3i? I have tried it but my pro numerals have had the wrong powers.

4. Re: Surd and Algebra Questions

Show us what you have done then...

5. Re: Surd and Algebra Questions

{} Is the square root sign. ' is to the power of. Sorry I don't know how to do the actual symbols.

6{162 c'7 d'5}
6{81x2xc'7xd'5}
6{ 81 x 2 x c'4 x c'3 x d'4 x d }
6{81 x c'4 x d'4} x {2 x c'3 x d}
54 c'2 d'2 x {2 x c'3 x d}

The answer is meant to be 54 c'3 d'2 x {2 x c x d}

6. Re: Surd and Algebra Questions

Originally Posted by Jerryjerry
{} Is the square root sign. ' is to the power of. Sorry I don't know how to do the actual symbols.

6{162 c'7 d'5}
6{81x2xc'7xd'5}
6{ 81 x 2 x c'4 x c'3 x d'4 x d }
6{81 x c'4 x d'4} x {2 x c'3 x d}
54 c'2 d'2 x {2 x c'3 x d}

The answer is meant to be 54 c'3 d'2 x {2 x c x d}
You're almost there. Just remember \displaystyle \begin{align*} \sqrt{c^3} = \sqrt{c^2 \cdot c} = \sqrt{c^2} \cdot \sqrt{c} = c \, \sqrt{c} \end{align*}. Apply this and then you'll be finished.

7. Re: Surd and Algebra Questions

Thank you so much for your time. I really appreciate your help.