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Find the cube roots of the following numbers.
(1) $8000$
(2) $729$
(3) $343$
(4) $-512$
(5) $-2744$
(6) $32768$

In the construction of quadrilateral ABCD, AB, BC, CD, AC and BD are given. Which of the following triangles cannot be drawn as the first step of construction?

Question 32

Factorise the following:

(i) $1–64a^3–12a+48a^2$



(ii) $8p^3+\frac{12}{5}{p}^2+\frac{6}{25}p+\frac{1}{125}$

What is the cube root of $-\frac{125}{512}$?

How does 'trading on equity' affect the choice of capital structure of a company? Explain with the help of a suitable example.

Find the smallest number by which 26244 should be divided so that the quotient is a perfect cube.

If the measures of the angles of a triangle are in the ratio 1:2:3, then how can the triangle be classified?

Rashi ordered pizza and coke for her friends. The bill appeared like this where two digits now represented by A and B, were not visible clearly.

$\begin{array}{ccc}A& 1& 2\\ +3& 1& B\\ 5& 2& 5\end{array}$

So she decided to find the two digits A and B. What would be the values of A and B?

Question 8

Write the correct answer from the given four options.

A square board has an area of 144 sq units. How long is each side of the board?

a) 11 units
b) 12 units
c) 13 units
d) 14 units

In the given figure, ABCD is a parallelogram. Find the values of x and y.

If ${4096}^{\frac{x}{4}}=512$, find the value of $x$.

Find Q in the addition.

$31Q+1Q3\underset{–}{}501\underset{–}{}$

Jack and Ruth went to a math amusement park. It was compulsory there to solve given math problem to enter into the park.

Simplify: $\sqrt{98}+\sqrt{50}-\sqrt{16}$

The rational number which is not lying between $\frac{5}{16}$ and $\frac{1}{2}$ is
$\left(a\right)\frac{3}{8}$

$\left(b\right)\frac{7}{16}$

$\left(c\right)\frac{1}{4}$

$\left(d\right)\frac{13}{32}$

Question 83

State whether the following statement is true or false:

Cube roots of 8 are + 2 and - 2

If 15 is added 10 times, it can be written as .

Find the volume of iron required to make an open box whose external dimensions are $36cm\times 25cm\times 16.5cm$ , the box being $1.5cm$ thick throughout. If $1c{m}^3$ of iron weighs $8.5$ grams, find the weight of the empty box in kilograms.

Question 122

Solve the following question:

Difference of two perfect cubes is 189. If the cube root of the smaller of the two numbers is 3, then find the cube root of the larger number.

Three nos. are in the ratio of 2:3:5. The sum of their cubes is 54880. Find the nos.

Hint: (2x)³ + (3x)³ + (5x)³ =54880

Expand the following identity.

​${(2x+1)}^3$

In a regular polygon, the ratio of the inner and outer angle is 14 : 4. How many sides does this polygon have ?

Suppose you and 7 of your friends ate a medium pizza cut into 8 equal parts. Since you all were still hungry you ordered one more pizza. This time a large pizza, which is again cut into 8 equal parts. The percentage of the full large pizza eaten by you will be _______.

Question 1
$\frac{8x-3}{3x}=2$ then find the value of $x$

What is the value 9.4 - 2.6?

Find the multiplicative inverse of ${10}^{-7}$.

The correct formula(s) to find the measure of interior angle of a $n-$sided regular polygon is/are:

Find the relation between $p$ and $q$ by simplifying the expression $(6p+5q{)}^2+(6p-5q{)}^2$.

Also, find the value of expression when $p^2=\frac{4}{9}$ and $q^2=\frac{2}{5}$.

Find the nearest integer to the square root of the following numbers

√728

A cuboid whose length, breadth and height are equal is called a ___________.

Simplify: $1.05\times 0.95$ using identities.

1. 27

If $x={\left(\frac{-2}{5}\right)}^{30}÷{\left(\frac{-2}{5}\right)}^{28}$ and $y={\left(\frac{-2}{5}\right)}^2\times {\left(\frac{-2}{5}\right)}^3$, then find the value of $(x^3÷y{)}^2$.

Take a two digit number 'ab' where a > b. When the difference between this number and the number obtained by reversing its digits is divided by 9, quotient will be equal to

Maturity value is equal to Total sum deposited + ___

In a building there are $24$ cylindrical pillars. The radius of each pillar is $28cm$ and height is $4m$. Find the total cost of painting the curved surface area of all pillars at the rate of $8$ per $m^2$

Under which of the following operations, are the integers not closed?

A micrometre screw gauge has a negative zero error of $0.0018cm$. The main scale reading is $3.6cm$ for an object. The baseline coincides with the ${45}^{th}$ division of the circular scale. Calculate the true length of the object in $cm$.