how to solve this without a calculator
sqrt (2009*2011*2015*2017+36)+10

Question

how to solve this without a calculator 
  sqrt (2009*2011*2015*2017+36)+10

nurali · Answer

Welcome to Openstudy.

anonymous · Answer

$$\sqrt{2009*2011*2015*2017+36}+10$$ 
how to describe simply

nurali · Answer

$$\sqrt{2009*2011*2015*2017+36}+10$$

$$4052159+10$$

$$4052169$$

skullpatrol · Answer

@Nurali all done without a calculator and a single word of $$\Huge 	ext{EXPLANATION}$$

anonymous · Answer

Write it using Latex ?

skullpatrol · Answer

Write what?

anonymous · Answer

Prime Factorization
Break all numbers down into prime factors, then match them.
$sqrt[100]=10 \times 10 = 2 \times 5 \times 2 \times 5$
There are two 2's and two 5's, therefore the answer is $2\times 5 = 10$

asnaseer · Answer

hint: try to first rewrite 2009, 2011, 2015 and 2017 in terms of 2013, e.g. 2009=(2013-4)

anonymous · Answer

OK I think expression under the root is a square.$$a=\frac{ 2009+2011+2015+2017 }{ 4 }=2013$$
2009⋅2011⋅2015⋅2017=(a−4)(a−2)(a+2)(a+4)
thanks.

anonymous · Answer

rest is simple: $$a=2013^{2}=4052169$$