1.Plot all the integers between -3 and 7 on a number line,by taking a suitable unit length on a number line
2.Find 3 rational numbers 1/7 and 1/3
3.Find any five rational numbers lying between 2/7 and 2/5
4.Find five rational number between 1/8 and 1/5
Answers
Between any two numbers there are infinitely many rational numbers.
We know that if a and b are rational then (a+b)/2 is rational and between them.
From 0.6 and 0.8, we get 0.7
Now we have 0.6 - 0.7 - 0.8
Now we find numbers between 0.6 and 0.7 and 0.7 and 0.8.
0.6 - 0.65 - 0.7 - 0.75 - 0.8
We can got answer 0.65, 0.7 and 0.75
We can continue to get
0.6 - 0.625 - 0.65 - 0.675 - 0.7 - 0.725 - 0.75 - 0.775 - 0.8
Like this we can go on adding numbers.
Alternate method: if we wish to find n numbers, find d=(b-a)/(n+1).
d(n+1)=b-a
So, b=a+(n+1)d.
Take numbers a, a+d, a+2d, a+3d, …, a+nd, a+(n+1)d. On all they are n+2 numbers in ascending order with a as first term and b as last term.
If we discard first and last number, we get n numbers between a and b.
Answer:
(-x) 1/3 = -(x 1/3).[1] For example: The cube root of -27 is written as [3]{-27} = -3 \). The cube root of -8 is written as \( \sqrt[3]{-8} = -2 \). The cube root of -64 is written as \( \sqrt[3]{-64} = -4 \).