This math topic focuses on solving advanced polynomial and quadratic expressions involving squared variables and coefficients under a square root. Problems require simplifying polynomial expressions, extracting square roots, and determining the values of variables (such as 'd', 'x', 'n', 'r', 'b') that satisfy the equations. The expressions are structured to challenge understanding of polynomial behavior, quadratic formulas, and algebraic manipulation without the use of a calculator. The skill level indicated is advanced, suitable for deeper comprehension and application of polynomials and quadratics concepts.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

more
View

Polynomial Algebra X plus 1 Squared - Squared Variables with Coefficient under Square Root - Solve Worksheet

Mobius Math Academy logo
Polynomial Algebra X plus 1 Squared - Squared Variables with Coefficient under Square Root - Solve
1
Find the value of q without using a calculator
A LaTex expression showing square root of 25q to the power of 2 + 50q + 25 = 75
a
q = 11
b
q = 13
c
q = 18
d
q = 12
e
q = 14
f
q = 21
2
Find the value of q without using a calculator
A LaTex expression showing square root of 25q to the power of 2 + 50q + 25 = 60
a
q = 12
b
q = 16
c
q = 7
d
q = 10
e
q = 13
f
q = 11
3
Find the value of w without using a calculator
A LaTex expression showing square root of 25w to the power of 2 + 50w + 25 = 90
a
w = 19
b
w = 21
c
w = 16
d
w = 17
e
w = 18
f
w = 10
4
Find the value of q without using a calculator
A LaTex expression showing square root of 4q to the power of 2 + 8q + 4 = 28
a
q = 13
b
q = 4
c
q = 10
d
q = 6
e
q = 15
f
q = 14
5
Find the value of w without using a calculator
A LaTex expression showing square root of 9w to the power of 2 + 18w + 9 = 36
a
w = 20
b
w = 7
c
w = 16
d
w = 2
e
w = 19
f
w = 11
6
Find the value of t without using a calculator
A LaTex expression showing square root of 9t to the power of 2 + 18t + 9 = 39
a
t = 12
b
t = 9
c
t = 17
d
t = 21
e
t = 14
f
t = 8
7
Find the value of n without using a calculator
A LaTex expression showing square root of 9n to the power of 2 + 18n + 9 = 33
a
n = 13
b
n = 11
c
n = 10
d
n = 9
e
n = 6
f
n = 8
8
Find the value of t without using a calculator
A LaTex expression showing square root of 16t to the power of 2 + 32t + 16 = 40
a
t = 13
b
t = 16
c
t = 7
d
t = 9
e
t = 2
f
t = 5