Respuesta :
Answer:
a)
Step-by-step explanation:
Square root of 75 (√75) is regarded as a surd function because the value inside the square root sign is not a perfect square. In that case the given value will be splitted into the product of a largest perfect square and a prime number as shown:
√75 = √3×25
√75 = √3×√25
√75 = √3 × 5
√75 = 5√3
a) Based on the above calculation, it can be inferred that his reasoning is incorrect. The value of 3 was supposed to be inside a square root not a whole number i.e √3 × √25
b) Since √75 = 5√3
√75 = 5 × 1.7321
√75 = 8.6605
√75 = 8.661 {to nearest thousand}
Answer:
Answer: √3 = 1.732
Step-by-step explanation:
Solution:-
- Jacob tries to estimate the square root of 75 and makes a calculation error. The following work was done by Jacob:
√75 = 3√25 = 3*5= 15
- The error was made by Jacob when he pulled out the constant " 3 " from under the root and missed to apply the property of square root on " 3 " itself.
- The correct version would be:
√75 = √3*√25 = √3*5
Answer: 5√3
- Now we will estimate the square root of 3 without using a calculator:
- We will first two per squares above and below " 3 " .
[ √4 = 2 , √1 = 1 ]
- From above we know that the square root lies within the range of [ 1 , 2 ].
- We also know that " √3 " would is closer to "√4 ". Hence, would be closer to 2 as compared to 1.
- We will take a guess of " 1.75 ", and square all guesses:
Guess 1: 1.75^2 = 3.0625
- The number is higher than "3" but very close. Guess a number lower than last one but closer to 1.75:
Guess 2: 1.73^2 = 2.9929
- The number is lower than "3" but very close. Guess a number higher than last one but closer to 1.73:
Guess 3: 1.735^2 = 3.010225
- The number is higher than "3" but very close. Guess a number lower than last one but closer to 1.735:
Guess 4: 1.7325^2 = 3.00155625
- The number is higher than "3" but very close. Guess a number lower than last one but closer to 1.7325:
Guess 4: 1.7323^2 = 3.00086329 ... Stop here
- Rounding the number to nearest thousandths we need to look at the 4th decimal place value of " 1.7323 ". The 4th decimal place has to be lower than 3 to get an exact √3.
- Hence, the answer to nearest thousandth would have all the 4th decimal places an onwards truncated. Therefore,
Answer: √3 = 1.732
