Question

Estimate the value of 101.4^0.5 +6.43^0 x 7.99^(2/3)

I’m not really sure of the answer, if you know, please tell me.

Answer 1

14

Explanation:

101.4^0.5 = 10.0697 etc

it says estimate so I'm going to round that to 10

6.43^0 Anything with an exponent of 0 = 1

7.99^(2/3) = 3.9966 etc you can round that to 4

Put in the values:

10 + 1 × 4

Use PEMDAS

Parentheses

Exponents

Multiplication

Division

Addition

We have to multiply 1 × 4 which is 4

We're left with 10 + 4 which is 14

Answer 2

14

Explanation:

`\sf 101.4^(0.5) +6.43^0 * 7.99^(\frac23)`

• 
  `\sf a^(0.5)=√(a)` so round 101.4 to 100 as the square root of 100 is easy to calculate mentally

• 
  `\sf a^0=1` so
  `\sf 6.43^0=1`

• 7.99 ≈ 8

• 
  `\sf a^(\frac23)=(a^(\frac13))^2`
• 
  `\sf8^(\frac13)` = the number that you cube to get 8

`\begin{aligned}\sf 101.4^(0.5) +6.43^0 * 7.99^(\frac23) & = \sf √(100) +1 *8^(\frac23)\\\sf & = \sf 10 + (8^(\frac13))^2\\& = \sf 10 + (2)^2\\& = \sf 10 + 4\\& = \sf 14\end{aligned}`