sqroot of( 10+2sqroot of 6+2sqroot of 10+2sqroot of 15) is equal to?

Answer 1

5.3823

Answer 2

Sqroot of( 10+2sqroot of 6+2sqroot of 10+2sqroot of 15)

Answer 3

let sq.root of Left hand side = (a)^(1/2) +(b)^(1/2) + (c)^(1/2)

if u square both sides,


10+ 2 sqrt 6 + 2 sqrt 10+ 2 sqrt 15= a+b+ c+ 2 sqrt ab+ 2 sqrt bc + 2 sqrt ca

now comparing surds on left to surds on right , and rational numbers,
a+b+ c= 10, ab=6,bc=10, ca = 15( u can take ab,cb,ca in any order as answer is commutative and doesnt require the order of a,b,c. )

find (ab)(bc)(ca)=(abc)^2 = 6*10* 15.

abc=900. u have ab= 6 ( in my example) , c= abc/ab

(from the above statement) c= 5,since bc=10 => b=2 and since ab =6 => a=3. therfore ans is

sqrt 2 + sqrt 3+ sqrt 5

Answer 4

Using the properties of radicals:
\/(10+2\/6+2\/10+2\/15) =
\/(10 + 2\/31) = \/10 + \/(2\/31)
\/10 + \/2*31 = \/10 + \/62 =
3,162 + 7,874 = 11,036
\/ = root
::

Answer 5

We know that:

(x+y+z)^2 = x^2 + y^2 + z^2 + 2xy + 2xz + 2yz

Or, sqrt(x^2 + y^2 + z^2 + 2xy + 2xz + 2yz) = +/-(x+y+z).....(#)

Now, substituting x = sqrt(2); y = sqrt(3); z = sqrt(5); we have:

( 10+2*sqrt(6) +2sqrt(10) +2sqrt(15))

= (2+ 3+ 5) +2*sqrt(2*3) +2sqrt(2*5) +2sqrt(3*5))

= (sqrt(2) + sqrt(3) + sqrt(3))^2

Consequently, by (#):

sqrt ( 10 +2sqrt(6) +2sqrt (10) +2sqrt(15))

= +/- (sqrt(2) + sqrt(3) + sqrt(3))

= +/- 5.38233235(correct to 8 places of decimals)

Answer 6

i got

[3 times the square root of 10] + [2 times the square root of 15] + [2 times the square root of 6]

because you cant add anything without the same radicand

Answer 7

Its seems to be a funny Question. Any way ????
Sq. Root of ( 10 + 2 Sq. root of 10 + 2 sq .root of 10 + 2 sq . root of 15 )

= Sq. root of (10 + 2 x 3.16228 + 2 x 3.87298 )

= Sq. root of ( 10 + 6.32456 + 7.74596)

= Sq. root of 24.07052

= 4.90617

Answer 8

Do you want an exact solution or just a solution?

Decimal solution: 4.194770823

Answer 9

If you want an exact answer, i don't know. But you can't simplify it anymore. So it stays just that.

Answer 10

here we use (a+b+c)square=a^2+b^2+c^2+2ab+2ac+2bc
nw 10=2+3+5
2squroot6=2*sqroot3*sqroot2=sqroot6
2squroot10=2*sqroot5*sqroot2=sqroot10
2squroot15=2*sqroot3*sqroot5=sqroot15
hence
sqroot3+sqroot2+sqroot5=sqroot(2+3+5+2(sqroot6+sqroot10+sqroot15))

Answer 11

=SQRT(10+2RT(10+2RT(15)))
=SQRT(10+2RT(10+7.745967))
=SQRT(10+8.425192)
=4.292457616
=4.293(3DP)

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