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Oksanka [162]
3 years ago
7

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

Mathematics
2 answers:
Cloud [144]3 years ago
6 0

9514 1404 393

Answer:

  (x^(1/2))^2 = x^(2/2) = x

Step-by-step explanation:

The square root of a number, when multiplied by itself, gives the original number.

  (√x)(√x) = x

The rule for exponents is that powers of the same base, when multiplied, will be the base to the sum of those powers.

  (a^b)(a^c) = a^(b+c)

Also, the first power of a number is that number itself.

__

  x^{\frac{1}{2}}\times x^{\frac{1}{2}}=x^{\frac{1}{2}+\frac{1}{2}}=x^1=x\\\\ \text{Compare to ...}\\\\ \sqrt{x}\times\sqrt{x}=x

MAXImum [283]3 years ago
3 0

Answer:

Squaring and square root are inverses, so one should "undo" the other. That is, squaring the square root of a number results in the number. Using the power of a power rule, you multiply the exponents. Since a number to the first power is itself, the product of the exponents must equal 1. This means that the power of the square root must be the reciprocal of 2, or one half.

Step-by-step explanation:

EDGE 2020-2021

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katen-ka-za [31]

Answer:

9³

Step-by-step explanation:

We know that,

a^b ÷ a^c = a^b^-^c

By following the above, let us solve the given question.

<u>Let us solve now.</u>

⇒ 9⁵ ÷ 9²

⇒ 9⁵⁻²

⇒<u> 9³</u>

7 0
3 years ago
On the first move, a game piece is moved ahead two spaces. On the next move, the game piece is moved ahead five spaces. What int
tatyana61 [14]

Answer: 7

Step-by-step explanation:

2+5=7

7 0
3 years ago
Answer asap pllllssssssss​
ch4aika [34]

Answer:

11x+3

Step-by-step explanation:

combine like terms

8x+3x = 11x

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11x+3

3 0
3 years ago
Read 2 more answers
Please answer this correctly
ozzi

Answer:

The range would decrease by 2

Step-by-step explanation:

The range is the difference between the highest number and the lowest number.

8 is the highest number and 1 is the lowest number here, so to find the range we would subtract 1 from 8.   8-1=7

But since 8 is being replaced by 6, we would subtract 1 from that instead.

6-1=5

The range decreased from 7 to 5, so it decreased by 2.

Hope that helps :)

6 0
3 years ago
Solve 729 s-⁵ = 3² (1-s) for S.​
sweet [91]

Answer:

No real solutions.

Step-by-step explanation:

729s^-5 = 729/s^5

729/s^5 = 3^2(1-s) = 9(1-s)

729=9(1-s)(s^5)

(1-s)(s^5)=81

s^5-s^6=81

Because 81 > 0 this means s^6 must be less than s^5. This is never possible as 6 is even so is always positive and is always greater in magnitude than s^5. The only time this isnt the case is when s is a decimal less than 1, but then the difference would be also less than 1 and not 81.

5 0
3 years ago
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