Evaluate the numerical expression: 18 - 3 * (4 + 2) + (-2)^3.
Real Numbers And Algebraic Calculations
Question · Easy
Factor it
Short
Calculate the exact numerical value of the expression: | -15 | - 2 * | 7 - 12 | + | -4 |^2.
What is the standard scientific notation of the decimal number 0.0000475?
Calculate the exact value of the expression: sqrt(196) - sqrt(81) + sqrt(256).
Expand and simplify the algebraic product using the difference of squares formula: (3x - 5)(3x + 5).
Would you rather: marbles
Expand and simplify the square of the binomial: (2a + 3b)^2.
Simplify the radical expression sqrt(72) by extracting all possible square factors from beneath the radical.
Simplify the exponential expression and compute its final numerical value: (2^5 * 2^7) / (2^3)^3.
Rationalize the denominator of the fraction 18 / sqrt(6) and state the result in simplest radical form.
Question · Medium
Rationalize the denominator and simplify: 12 / (sqrt(7) - sqrt(3)).
Expand and simplify the algebraic expression: (sqrt(7) - 2)^2 + 4*sqrt(7).
Calculate the exact value of the expression: sqrt((2 - sqrt(5))^2) - sqrt(5).
Simplify the algebraic fraction (6x^2 - 18x) / (9x) for all non-zero real numbers x.
Simplify the algebraic fraction (x^2 - 16) / (3x + 12) for all real x != -4.
Simplify the algebraic fraction (x^2 - 5x + 6) / (x^2 - 9) for all real numbers x not in {-3, 3}.
Perform the subtraction and simplify: 3 / (x - 2) - 12 / (x^2 - 4) for all real x not in {-2, 2}.
Perform the multiplication and state the result in simplest form: ((x^2 - 4) / (x^2 + 3x)) * ((x + 3) / (x - 2)) for all real x not in {-3, 0, 2}.
Calculate the exact numerical value of the expression: (2/5)^(-2) * (4/25) + 3^(-1).
Which of the following real numbers has the greatest numerical value: 3*sqrt(5), 4*sqrt(3), 2*sqrt(11), or 7?
Evaluate the nested radical expression: sqrt(14 - 6*sqrt(5)) + sqrt(14 + 6*sqrt(5)).
Question · Hard
If a non-zero real number x satisfies x + 1/x = 6, what is the exact value of x^2 + 1/x^2?
Expand and simplify the algebraic expression: (x + 3)^3 - (x - 3)^3.
Determine the maximal domain of definition (D) in R for the algebraic expression: E(x) = sqrt(2x - 8) / (x - 6).
Simplify the complex rational expression for all real numbers x not in {-1, 0, 1}: ((x + 1)/(x - 1) - (x - 1)/(x + 1)) : (4x / (x^2 - 1)).
Solve the linear equation in R: 4(2x - 3) - 3(x - 2) = 14.
Equations Inequalities And Systems
Find the complete solution set in R of the incomplete quadratic equation: 5x^2 - 80 = 0.
Find all real solutions to the equation: 3x^2 - 15x = 0.
Solve the linear inequality in R: 7 - 3x <= 19.
Given the linear system of equations { x + y = 14, x - y = 6 }, what is the product x * y?
Calculate the discriminant (Delta) of the quadratic equation: 3x^2 - 7x + 2 = 0.
What is the smallest integer that satisfies the inequality: 4x - 9 > 7?
Find the real roots of the quadratic equation: x^2 - 9x + 20 = 0.
Solve the quadratic equation in R: 2x^2 + 5x - 3 = 0.
Using Viète's formulas, find the sum (S) and product (P) of the roots of the quadratic equation: 2x^2 - 10x + 7 = 0.
If x1 and x2 are the roots of the quadratic equation x^2 - 8x + 5 = 0, what is the value of x1^2 + x2^2?
Solve the linear equation with fractions: (2x - 1)/3 - (x + 2)/4 = 1.
Solve the linear system { 3x + 2y = 19, 2x - y = 8 } and find the value of x + y.
A father is currently 36 years old and his son is 8 years old. In how many years will the father's age be exactly three times the son's age?
A student purchased 4 notebooks and 3 pens for 58 lei. Another student bought 2 notebooks and 5 pens of the same type for 50 lei. What is the price of one notebook?
Find the solution set in R of the system of linear inequalities: { 3x - 5 < 7, 2x + 1 >= -3 }.
Solve the double inequality in R: -5 < 3x + 1 <= 10.
How many integer solutions satisfy the system of inequalities: { 2x + 7 > 1, 5 - x >= 1 }?
For what real value of the parameter m does the quadratic equation x^2 - 10x + m = 0 have exactly one double real root?
Factor the quadratic trinomial 3x^2 - 10x + 3 into a product of linear factors.
Solve the rational equation in R: x / (x - 3) + 2 / (x + 3) = 18 / (x^2 - 9).
Find the complete solution set in R of the absolute value equation: |2x - 3| = x + 3.
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