Explain why the square root of a number is defined to be equal to that number to the 1/2 power

Question

Explain why the square root of a number is defined to be equal to that number to the 1/2 power

in progress 0
Neala 5 years 2021-08-27T07:55:23+00:00 1 Answers 55 views 0

Answers ( )

  1. Helga
    0
    2021-08-27T07:56:25+00:00
    Reply

    9514 1404 393

    Answer:

      (x^(1/2))(x^(1/2)) = x^(1/2 +1/2) = x^1 = x

    Step-by-step explanation:

    The rule of exponents is …

      (x^a)(x^b) = x^(a+b)

    From which …

      (x^a)(x^a) = x^(a+a) = x^(2a)

    So, if we want two identical factors that have a product of x = x^1, then the exponents of those factors will be such that …

      x^(2a) = x^1

      2a = 1

      a = 1/2

    The square root is defined as one of two identical factors that have a product equal to the specified value. That is …

      (√x)(√x) = x

    Above, we have shown that …

      (x^(1/2))(x^(1/2)) = x

    so, we can conclude …

      √x = x^(1/2)

    _____

    Additional comment

    In like fashion, we can show that the n-th root of a number is the same as that number to the 1/n power. It’s really a matter of definition. Since the square of x^(1/2) is x, we call x^(1/2) the square root. It is used commonly enough that it has its own symbol: √x.

Leave an answer

Browse

Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )