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iris [78.8K]
3 years ago
14

Approximate using perfect squares what is the radical symbol 78

Mathematics
1 answer:
Evgen [1.6K]3 years ago
8 0

The <em><u>correct answer</u></em> is:

The estimate is between 8 and 9.

Explanation:

Perfect squares are numbers whose square roots are whole numbers.  78 is not one; however, it is between two others, namely 64 and 81.

64 is the perfect square of 8, since 8(8) = 64.

81 is the perfect square of 9, since 9(9) = 81.

78 is between these two; since it is closer to 81, this means the answer will be a decimal between 8 and 9, but that is closer to 9.

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3 years ago
Apply division algorithm to find the quotient and remainder on dividing the polynomial 3 x^ + 4 x^ square + 6 x + 9 by x^ + 3x +
Ulleksa [173]

I suppose you mean

\dfrac{3x^3+4x^2+6x+9}{x^2+3x+7}

3x^3=3x\cdot x^2, and if we multiply x^2+3x+7 by 3x we get 3x^3+9x^2+21x. Subtracting this from the numerator gives a remainder of -5x^2-15x+9.

-5x^2=-5\cdot x^2, and multiplying x^2+3x+7 by -5 gives -5x^2-15x-35. Subtracting this from the previous remainder gives a new remainder of 44.

44 has no remaining factors of x^2 in it, so we're done, and

\dfrac{3x^3+4x^2+6x+9}{x^2+3x+7}=\underbrace{3x-5}_{\rm quotient}+\dfrac{\overbrace{44}^{\rm remainder}}{x^2+3x+7}

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