Exponentiation + square root - math problems

If n is a positive integer and x is any real number, then x^n corresponds to repeated multiplication x^n=x×x×⋯×x (n times). We can call this “x raised to the power of n,” “x to the power of n,” or simply “x to the n.” Here, x is the base, and n is the exponent or the power.

Number of problems found: 32

• What is
What is the annual percentage increase in the city when the population has tripled in 20 years?
• Volume of wood
Every year, at the same time, an increase in the volume of wood in the forest is measured. The increase is regularly p% compared to the previous year. If in 10 years the volume of wood has increased by 10%, what is the number p?
• The tickets
The tickets to the show cost some integer number greater than 1. Also, the sum of the price of the children's and adult tickets, as well as their product, was the power of the prime number. Find all possible ticket prices.
• Three members GP
The sum of three numbers in GP (geometric progression) is 21 and the sum of their squares is 189. Find the numbers.
• Exponential equation
Find x, if 625 ^ x = 5 The equation is exponential because the unknown is in the exponential power of 625
• Unknown number 17
Milada said, I am thinking of a number such that I evaluate expression x1/3, the value of the expression would be 5. Which number Milada thinking?
• Unknown number 7
Calculate unknown number whose 12th power when divided by the 9th power get a number 27 times greater than the unknown number. Determine the unknown number.
• Gp - 80
Sum of the first four members of a geometric progression is 80. Determine they if we know that the fourth member is nine times greater than the second.
• Cube 6
Volume of the cube is 216 cm3, calculate its surface area.
• TV transmitter
The volume of water in the rectangular swimming pool is 6998.4 hectoliters. The promotional leaflet states that if we wanted all the pool water to flow into a regular quadrangle with a base edge equal to the average depth of the pool, the prism would have
• Chord AB
What is the length of the chord AB if its distance from the center S of the circle k(S, 92 cm) is 10 cm?
• Digits A, B, C
For the various digits A, B, C is true: the square root of the BC is equal to the A and sum B+C is equal to A. Calculate A + 2B + 3C. (BC is a two-digit number, not a product).
• Geometric sequence
In the geometric sequence is a4 = 20 a9 = -160. Calculate the first member a1 and quotient q.
• 3d vector component
The vector u = (3.9, u3) and the length of the vector u is 12. What is is u3?
• Computer
The computer was purchased 10000,-. Each year, the price of a computer depreciates always the same percentage of the previous year. After four years, the value of the computer is reduced to 1300,- How many percent was depreciated price of the computer eac
• Roots
Calculate the square root of these numbers:
• Prism X
The prism with the edges of the lengths x cm, 2x cm and 3x cm has volume 20250 cm3. What is the area of surface of the prism?
• Balls
Three metal balls with volumes V1=71 cm3 V2=78 cm3 and V3=64 cm3 melted into one ball. Determine it's surface area.
• Geometric sequence 3
In geometric sequence is a8 = 312500; a11= 39062500; sn=1953124. Calculate the first item a1, quotient q and n - number of members by their sum s_n.
• Rhombus
Find the length of the other diagonal and area of rhombus. The perimeter of a rhombus is 40 cm and one of the diagonals is of length 10 cm.

Do you have an interesting mathematical word problem that you can't solve it? Submit a math problem, and we can try to solve it.

We will send a solution to your e-mail address. Solved examples are also published here. Please enter the e-mail correctly and check whether you don't have a full mailbox.

Please do not submit problems from current active competitions such as Mathematical Olympiad, correspondence seminars etc...