Maths question

[Mllcg]

can someone explain why the answer is not 16?(which was what i guessed as well)

 

Edited November 3, 2011 by Mllcg

[West_end]

9 + 16 = 25

[Happily1986]

can someone explain why the answer is not 16?(which was what i guessed as well)

 

 

This is a infinite series of squares,

 

1,4,9,16,25,36,49,64,81,100....

 

The answer must be a sum of any two elements which have to be found in the series above. This implies some combination at work.

 

16 is NOT a sum of any two possible elements.

 

1+1=2

1+4=5

1+9=10

4+4=8

4+9=13

9+9=18

 

The above represent the possible pairs that could have yield anything from 0 to 18 and 16 is not one of them. On the contrary, 25=16+9. So 25 is the answer.

Edited November 3, 2011 by Happily1986

[Mllcg]

This is a infinite series of squares,

 

1,4,9,16,25,36,49,64,81,100....

 

The answer must be a sum of any two elements which have to be found in the series above. This implies some combination at work.

 

16 is NOT a sum of any two possible elements.

 

1+1=2

1+4=5

1+9=10

4+4=8

4+9=13

9+9=18

 

The above represent the possible pairs that could have yield anything from 0 to 18 and 16 is not one of them. On the contrary, 25=16+9. So 25 is the answer.

 

i was thinking of 8s all the way. what did i do wrong?

[Happily1986]

i was thinking of 8s all the way. what did i do wrong?

 

8 is not a square. i bet you were thinking 8+8=16. A number that has to be expressed as a surd is not a perfect square (8 =2*sqrt of 2) and in this case, the answer has to be a sum of 2 perfect squares whatever they are.

[Mllcg]

8 is not a square. i bet you were thinking 8+8=16. A number that has to be expressed as a surd is not a perfect square (8 =2*sqrt of 2) and in this case, the answer has to be a sum of 2 perfect squares whatever they are.

2^4=16

8+8=16?

 

wrong?

[Fastfive1]

can someone explain why the answer is not 16?(which was what i guessed as well)

 

 

It's a confusing question that requires you to think carefully.

 

49= (2x2)+(2x2)+(3x3)+(4x4)+(4x4) or (5x5)+(4x4)+8

36= (2x2)+(3x3)+(4x4)+7

25= (3x3)+(4x4)

16= (2x2)+(3x3)+3 or (2x2x2x2) or (2x8) or (4x4)

 

Based on these permutations, 16 is definitely out along with 36 and 49. There's a difference between multiply and addition. What went through your head was probably 16=4x4

Which can be broken down in to 2x2x2x2 because 4 can be square rooted.

 

The sum of two smaller square numbers refer to two numbers (9 and 16) that were a result of squaring (3 to form 9 and 4 to form 16) before adding them up to form a new value(25).

[Fastfive1]

2^4=16

8+8=16?

 

wrong?

 

Err 8 is 2x2x2

so 16 is (2x2x2) +(2x2x2).

Dude you need tuition....

[1fast1]

can someone explain why the answer is not 16?(which was what i guessed as well)

 

Pythagorean Triple

[SimonTan]

again the english understanding comes into play.

 

"The sum of two smaller square number" is vague.

 

It could mean 4 + 4 + 4 + 1 + 1 + 1 +1 = 16

 

It did not specify how many TIMES each smaller square number can be used in the summation process.

 

 

[Kotila]

Good ans.

[SimonTan]

Wah.....respect....certain MCForumers really got the ink!

 

 

Pythagorean Triple

 

[Fastfive1]

Pythagorean Triple

 

Ahh yes this is what we use to calculate the length of one side of a right angled triangle when we're given the length of two other sides.

Edited November 4, 2011 by Fastfive1

[Sk65]

square number

 

1sq = 1

2sq = 4

3sq = 9

4sq = 16

5sq = 25

 

answer

a=16 ( 4sq , i.e. possible combinations = 1sq + 1sq or 1sq + 2sq or 1sq + 3sq or 2sq + 2sq or 2sq + 3sq or 3sq + 3sq (2,5,10,8,13,18) i.e. all cannot) so wrong aswer

b=25 (5sq, i.e. ...)

c=36 (6sq, i.e. ...)

d=49 (7sq, i.e. ...)

 

 

 

i think given the pressure of limited time,

very stressful question

 

[Sk65]

again the english understanding comes into play.

 

"The sum of two smaller square number" is vague.

 

It could mean 4 + 4 + 4 + 1 + 1 + 1 +1 = 16

 

It did not specify how many TIMES each smaller square number can be used in the summation process.

 

 

like that say, no ending liao la

any number can be

1+1+1+1+1+1+1.......

[1fast1]

Ahh yes this is what we use to calculate the length of one side of a right angled triangle when we're given the length of two other sides.

 

Actually that's Pythagoras Theorem. a^2 + b^2 = c^2, where a and b are the lengths of the perpendicular segments of a right triangle, and c is the length of the hypotenuse (longest "slanting" side). Holds for any value of a and b (integer and non-integer), and c is often not a whole number (integer) even when a and b are integers - it's often irrational.

 

Pythagorean triples are a related concept. a^2 + b^2 = c^2 still holds, but here, a, b and c are constrained to be whole numbers (all greater than zero). The geometric interpretation is one of right triangles with all the sides having integer lengths.

 

The most "fundamental" pythagorean triples are called primitive pythagorean triples, where a,b and c share no common factors higher than one (are coprime), but I'll stop boring you now.

Edited November 4, 2011 by Turboflat4

[Fastfive1]

Actually that's Pythagoras Theorem. a^2 + b^2 = c^2, where a and b are the lengths of the perpendicular segments of a right triangle, and c is the length of the hypotenuse (longest "slanting" side). Holds for any value of a and b (integer and non-integer), and c is often not a whole number (integer) even when a and b are integers - it's often irrational.

 

Pythagorean triples are a related concept. a^2 + b^2 = c^2 still holds, but here, a, b and c are constrained to be whole numbers (all greater than zero). The geometric interpretation is one of right triangles with all the sides having integer lengths.

 

The most "fundamental" pythagorean triples are called primitive pythagorean triples, where a,b and c share no common factors higher than one (are coprime), but I'll stop boring you now.

 

When i last used that formula 3 years ago, the math questions usually had nice numbers that could fit perfectly into the equation without some number with decimals after being square rooted.

[Happily1986]

Actually that's Pythagoras Theorem. a^2 + b^2 = c^2, where a and b are the lengths of the perpendicular segments of a right triangle, and c is the length of the hypotenuse (longest "slanting" side). Holds for any value of a and b (integer and non-integer), and c is often not a whole number (integer) even when a and b are integers - it's often irrational.

 

Pythagorean triples are a related concept. a^2 + b^2 = c^2 still holds, but here, a, b and c are constrained to be whole numbers (all greater than zero). The geometric interpretation is one of right triangles with all the sides having integer lengths.

 

The most "fundamental" pythagorean triples are called primitive pythagorean triples, where a,b and c share no common factors higher than one (are coprime), but I'll stop boring you now.

were you a maths or stats major?