Melody

Mmm 

Which is greater,  10% of nothing OR 100% of nothing ???     

Mmm

the sqrt and the square cancel each other out so the problem becomes

$$\{[(log_{10}(10^{10})^3]^3\}^3\\\\
=\{[(log_{10}(10^{30})]^3\}^3\\\\
=\{[30(log_{10}(10)]^3\}^3\\\\
=\{[30(1)]^3\}^3\\\\
=[30]^9\\\\
=3^9*10^9\\\\
=19683*10^9\\\\\
=1.9683*10^{13}$$

There you go, multiple choice answers - take your pick   

Use the calc on the home page

Thanks Thejamesmachine, 

Thats a neat summary of factor shortcuts.  I had not seen the 7 one before!

$$\\3\sqrt{12}*2\sqrt6\\
=3*2*\sqrt{12}*\sqrt6\\
=6\sqrt{72}\\
=6\sqrt{36*2}\\
=6*6\sqrt{2}\\
=36\sqrt{2}\\$$

10 + 15sqrt(5)/sqrt5-2

=10 + (15sqrt(5)/sqrt5)-2

=10+15-2

=23

What, do you mean on this calculator?

6C4 is entered in the input box as    nCr(6,4)

I think there are other ways to enter it too but that is how I do it :)

$$\\16500=30000(1-r)^8\\\\
0.55=(1-r)^8\\\\
0.55^{1/8}=1-r\\\\
r=1-0.55^{1/8}$$

$${\mathtt{1}}{\mathtt{\,-\,}}{{\mathtt{0.55}}}^{\left({\frac{{\mathtt{1}}}{{\mathtt{8}}}}\right)} = {\mathtt{0.072\: \!005\: \!641\: \!200\: \!676\: \!8}}$$

$$r\approx 0.072\qquad $this is 7.2\%$$$

$$\\1000=16500(1-0.072)^n\\\\
0.060606060=0.928^n\\\\
log(0.060606060)=log(0.928^n)\\\\
log(0.060606060)=nlog(0.928)\\\\
n=\frac{log(0.060606060)}{log(0.928)}$$

$${\mathtt{n}} = {\frac{{log}_{10}\left({\mathtt{0.060\: \!606\: \!06}}\right)}{{log}_{10}\left({\mathtt{0.928}}\right)}} \Rightarrow {\mathtt{n}} = {\mathtt{37.516\: \!425\: \!994\: \!501\: \!126\: \!2}}$$

2015+37.5 = 2052 

Mmm looks a bit suspect.

you better check it!

If the long side squared = the sum of the 2 short sides squared then it MUST be a right angled triangle.

Yep must be the red !