Question

4 - 1/5
how to solve it​

Answer 1

$4 - \frac{1}{5} = \frac{20}{5} - \frac{1}{5} = \frac{19}{5}$

Answer 2

Step-by-step explanation:

How do I calculate 4^1.5 without using a calculator?

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55 Answers

John Lind, BS Physics & Mathematics, Arizona State University (1976)

Answered August 17, 2019

Simple enough for me to do in my head.

Has two answers: 8, and -8

The number, 1.5 is the same as 3/2 (three halves). A fractional power is a root; i.e. x^(1/2) or x^(0.5) is, by definition, the square root of x.

4^1.5 is 4^(3/2), the square root of four cubed. Doesn’t matter if you take the square root first or do the cube operation first.

4^(1/2) = 2, and -2

2^3 = 8, and (-2)^3 = -8

Doing the other operation first:

4^3 = 64

64^(1/2) = 8, and -8

This has two answers due to the square root, with the sign carrying through when the result of that is cubed: 8 and -8, or emerging after cubing first and then taking hte square root. Working the problem in reverse using the two answers:

8^(1/3) = 2, and 2^2 = 4, or

8^2 = 64, and 64^(1/3) = 4

-8(1/3) = -2, and -2^2 = 4, or

-8^2 = 64, and 64^(1/3) = 4

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