I need someone to check a few answers for me, please!
1. Which expression has an approximate value between 6 and 7? Select two answers.
A. √36***
B. √38
C. √42***
D. √50
2. How many decimal places does an irrational number have?
A. zero
B. one
C. infinite***
D. between one and ten
3. Determine if each root is a rational or irrational number. Explain your reasoning.
A- √36
B- √78 (this is supposed to have a 3 in the corner of it)
I think these are both irrational numbers but don't know how to explain it.
So, would #1 be 38 and 42?
And for #3, A would be rational and B wouldn't, right?
correct
Thank you~!
Okay! So I know how to explain number 3, I just need to know if they're irrational numbers or not!
#1 not A -- √36 = 6
and 7^2 = 49
so pick another number between 36 and 49
#2 ok
#3 see A -- 6 is rational
also, note that
4^3 = 64
5^3 = 125
so 78 is not a perfect cube. Its cube root is irrational
Sure, let me help you with those answers!
1. The expressions that have an approximate value between 6 and 7 are A. √36 and C. √42. Both of these square roots are between 6 and 7 on the number line.
2. An irrational number has an infinite number of decimal places. So the correct answer is C. infinite.
3. A. √36 is actually a rational number. The square root of 36 gives you 6, which is a whole number and therefore rational.
B. √78 (with 3 in the corner) is indeed an irrational number. The square root of 78 cannot be simplified to a whole number or a fraction. It will result in a never-ending decimal.
Hope that helps, and remember, math can be quite irrational at times!
Sure! I can help you check your answers and explain the reasoning behind them.
1. Which expression has an approximate value between 6 and 7? Select two answers.
To determine which expressions have an approximate value between 6 and 7, we can calculate their actual values and see which ones fall in that range.
A. √36 = 6
B. √38 ≈ 6.1644
C. √42 ≈ 6.4807
D. √50 ≈ 7.0711
Based on the calculations, expressions A and C have values between 6 and 7. Therefore, the correct answers are A and C.
2. How many decimal places does an irrational number have?
An irrational number is a number that cannot be expressed as a fraction or a terminating or recurring decimal. It is a non-repeating, non-terminating decimal. Since irrational numbers cannot be expressed exactly as a fraction, they have an infinite number of decimal places. Therefore, the correct answer is C - infinite.
3. Determine if each root is a rational or irrational number. Explain your reasoning.
A. √36
To determine if √36 is a rational or irrational number, we can check if 36 is a perfect square. Since 36 is a perfect square (6^2 = 36), the square root of 36 (√36) is a rational number. So, A - √36 is a rational number.
B. √78
To determine if √78 is a rational or irrational number, we can check if 78 is a perfect square. Since 78 is not a perfect square, the square root of 78 (√78) is an irrational number. So, B - √78 is an irrational number.
The reasoning behind this is that if a number can be expressed as a fraction or a terminating or recurring decimal, it is rational. If it cannot be expressed in these forms, it is irrational.