Radical Calculations

Algebra Level 1

Find the value of
$\displaystyle \sqrt {13-\sqrt{11+\sqrt{15+2\sqrt{16+\sqrt{81}}}}}$

5 3 6 2 9 0 1

3 solutions

Chew-Seong Cheong
Jan 25, 2015

$\sqrt{13-\sqrt{11+\sqrt{15+2\sqrt{16+\sqrt{81}}}}}$

$=\sqrt{13-\sqrt{11+\sqrt{15+2\sqrt{16+9}}}}$

$=\sqrt{13-\sqrt{11+\sqrt{15+2\sqrt{25}}}}$

$=\sqrt{13-\sqrt{11+\sqrt{15+10}}}$

$=\sqrt{13-\sqrt{11+\sqrt{25}}}$

$=\sqrt{13-\sqrt{11+5}}$

$=\sqrt{13-\sqrt{16}}$

$=\sqrt{13-4}$

$=\sqrt{9}$

$=\boxed{3}$

Thank You !!

Jomari Ubas - 6 years, 4 months ago

Nathan King
Jan 29, 2015

All of this is supposed to make you think that the answer is 3, but there are actually many different answers to this problem.

Take the first part for example. Sqrt of 81 is not only 9, but also -9 which would turn the next part into the sqrt of 7.

Each time you have a positive on the inside of a square root, you have a positive and negative answer.

No the square root of a positive number is positive. (You are referring to solutions of x^2=81 and similar equations... There is a reason why you there specify using the "plusminus" sign that there are two solution...namely that the square root is 9 only...

Jim Lindholm - 6 years, 4 months ago

You just proved my point by saying that x^2=81. That means that both -9 and 9 are both answers to be squared into 81. Therefore the square root of 81 is both 9 and -9 making the next part the square root of (16+9) AND (16-9). So, you now have to take the next step of the square root of 15 + 2 (previous answer). So you have 4 answers to this part because each of the previous answers is still positive inside the radical which makes there be both a positive and a negative answer for each.

Nathan King - 6 years, 4 months ago

It is not possible yo square root negetive number

Ishmam Uddin - 6 years, 4 months ago

Yes it is, you use the number i.

Conor Cooley - 6 years, 4 months ago

Bala Murugan
Jan 27, 2015

solve it from backwards ,that is it!

Radical Calculations

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