x = 7
Restricting the discussion to real numbers for now. In this case, the square root is only defined for non-negative numbers; the principal square root of a positive number is the POSITIVE square root. For example, both +5 and -5 are square roots of 25, since both - when squared - give you 25. But the positive square root (+5) is called the principal square root, and if you write the square root symbol, that's the number usually meant.
X = 81 sqrt(X) + 3 = 12 ( subtract 3 from each side ) sqrt(X) = 9 (square both sides ) X = 81 ( the square root of 81 is 9 )
It is x*sqrt(x) or x^(3/2)
x^(3) + 125 => x^(3) + 5^(3) This factors to (x + 5)(x^(2) - 5x + 5^(2) ) or (x + 5)(x^(2) - 5x + 25) NB The clue is to spot that the constant (125) is a cubic numbers ( 5^(3)). Similarly with other 'cubic factorings'.
3 x 5 cm = area 15 square cm BUT a shape 3 x 5 is not a square, it is a rectangle. A square would either be 3 x 3 or 5 x 5 size.
3(x-5)^0.5 = 3 First divide both sides by 3 so that (3(x-5)^0.5)/3 = 3/3 (x-5)^0.5 = 1 Then square both sides ((x-5)^0.5)^2 = 1^2 (x-5)^1 = 1 x-5 = 1 Then add five to both sides x-5+5 = 1 +5 x+0 = 6 x = 6
5
There are: 5*3 = 15 square feet
-2 and -3Check:(-2) + (-3) = -5(-2)(-3) = 6Thus -2 and -3 are not the required numbers. let's find them: x + y = -6xy = -5 y = -x -6x(-x - 6) = -5-x^2 - 6x = -5x^2 + 6x = 5x^2 + 6x + 9 = 5 + 9(x + 3)^2 = 14x + 3 = (+ & -)square root of 14x = -3 (+ & -)square root of 14x = -3 + square root of 14 or x = - 3 - square root of 14y = -x - 6y = 3 - square root of 14 - 6 or y = 3 + square root of 14 - 6y = -3 - square root of 14 or y = -3 + square root of 14Check:(-3 + square root of 14) + (-3 - square root of 14) = -6(-3 + square root of 14)(-3 - square root of 14) = -5 ?(-3)^2 - (square root of 14)^2 = -5 ?9 - 14 = -5Check also tow other numbers.
You have : ----------------- 5 = ( x ) ( 3 )^1/2 x = ( 5 ) / ( 3 )^1/2 = +/- 2.887 <-----------------------
5 m x 3 m = 15m2
15 square feet
A factor tree tells you the prime factorization. The prime factorization can indicate a square number. Square numbers have even pairs of prime factors. 2 x 2 x 3 x 3 is a square number. 5 x 5 x 5 x 5 x 7 x 7 x 7 x 7 is a square number.
3 sqrt -5 = 3 x 5i = 15i; 3 sqrt 9 = 3 x 3 = 9 so full answer is 135i where i is the sqrt of -1
√(3x - 5) = 3 ∴3x - 5 = 9 ∴3x = 14 ∴x = 14/3
3 x 5 in inches is 15 square inches.