7

Q1. Show that when a number is trebled, its cube is 27 times the cube of the given number.

Solution

Let the given number be p and let q denote the treble of p, i.e., q = 3p Now, q³ = q q q = 3p 3p 3p = 3 3 3 p p p = 27 p3 Thus, q³ = 27 (cube of p)

Q2. Evaluate

Solution

= = 125a² - 5a²= 120a²

Q3. Find: using:  

Solution

Using the given pattern, we have

Q4. What is 3 into the cube root of seven?

Solution

3 into the cube root of 7

Q5. (a) If x² ends with 5, then with which number will x³ end? (b) If y³ ends with 8, then with which number will y² end?

Solution

(a) Given that, x² ends with 5. We know that if a square number ends with 5, then its square root also ends with 5. So, x will end with 5. Also, we know that the cube of a number ending with 5 also ends with 5. Thus, x³ will end with 5. (b) Given that, y³ ends with 8. We know that if a cube number ends with 8, then its cube root ends with 2. So, y will end with 2. Also, we know that the square of a number ending with 2 ends with 4. Thus, y² will end with 4.

Q6. If  = 16, then =? 

• 1) 46
• 2) 56
• 3) 36
• 4) 26

Solution

Using the estimation method, 8 < 17 < 27, i.e. 2³ < 17 < 3³. Hence,  = 26

Q7. Find the cubes of the following numbers: i) ii) 0.06 iii)  

Solution

i)     ii) 0.06 =   iii)

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