Simplify sqrt-54 using the imaginary number i A) 3isqrt6 B) -3sqrt6 C) isqrt54 D) 3sqrt-6

Simplify sqrt-54 using the imaginary number i A) 3isqrt6 B) -3sqrt6 C) isqrt54 D) 3sqrt-6

Question
Exponents and radicals
asked 2021-01-08
Simplify sqrt-54 using the imaginary number i
A) \(\displaystyle{3}{i}\sqrt{{6}}\)
B) \(\displaystyle-{3}\sqrt{{6}}\)
C) \(\displaystyle{i}\sqrt{{54}}\)
D) \(\displaystyle{3}\sqrt{-}{6}\)

Answers (1)

2021-01-09
For a>0, \(\displaystyle√-{a}={i}√{a}\). Hence, \(\displaystyle√-{54}={i}√{54}={i}√{9}\cdot{6}={i}√{9}\cdot√{6}={i}{\left({3}\right)}\cdot√{6}={3}{i}√{6}\)
So, the answer is choice A.
0

Relevant Questions

asked 2021-05-01
Find all zeros of p(x), real or imaginary. \(p(x) = x^{4} + 6x^{3} + 6x^{2} -18x -27\) List all of the possible rational zeros according to the rational zero theorem and state the values for C, A, B and D in the following partial factorization of \(p(x) = (x-c)(x^{3}+Ax^{2}+Bx+D)\) State the exact answer and a decimal approximation of each zero to the tenths place
asked 2020-11-02
\(\displaystyle{6}^{{2}}\)
=
A. 36
B. 12
C. 66
D. 30
asked 2021-05-16
Consider the curves in the first quadrant that have equationsy=Aexp(7x), where A is a positive constant. Different valuesof A give different curves. The curves form a family,F. Let P=(6,6). Let C be the number of the family Fthat goes through P.
A. Let y=f(x) be the equation of C. Find f(x).
B. Find the slope at P of the tangent to C.
C. A curve D is a perpendicular to C at P. What is the slope of thetangent to D at the point P?
D. Give a formula g(y) for the slope at (x,y) of the member of Fthat goes through (x,y). The formula should not involve A orx.
E. A curve which at each of its points is perpendicular to themember of the family F that goes through that point is called anorthogonal trajectory of F. Each orthogonal trajectory to Fsatisfies the differential equation dy/dx = -1/g(y), where g(y) isthe answer to part D.
Find a function of h(y) such that x=h(y) is the equation of theorthogonal trajectory to F that passes through the point P.
asked 2021-03-04
Simplify each of the following expressions. Be sure that your answer has no negative or fractional exponents. \(a*(1/81)^(-1/4)b*x^(-2)y^(-4)c*(2x)^(-2)(16x^2y)^(1/2)\)
asked 2021-01-31
Radical and Exponents Simplify the expression \(\frac{(ab^2 c^-3}{2a^3 b^-4)}^{-2}\)
asked 2021-03-09
Simplify: \(\displaystyle{\left({7}^{{5}}\right)}{\left({4}^{{5}}\right)}\). Write your answer using an exponent.
Explain in words how to simplify: \(\displaystyle{\left({153}^{{2}}\right)}^{{7}}.\)
Is the statement \(\displaystyle{\left({10}^{{5}}\right)}{\left({4}^{{5}}\right)}={14}^{{5}}\) true?
asked 2021-01-17
Rewrite the following expressions without using radicals or negative exponents. Simplify when possible. \(\displaystyle{\sqrt[{{5}}]{{{x}^{{20}}{y}^{{-{{4}}}}}}}\)
asked 2021-04-23
Suppose that x represents the larger of two consecutive odd integers.
a. Write a polynomial that represents the smaller integer.
b. Write a polynomial that represents the sum of the two integers. Then simplify.
c. Write a polynomial that represents the product of the two integers. Then simplify.
d. Write a polynomial that represents the difference of the squares of the two integers. Then simplify
asked 2021-03-11
in number 7, Is the exponent of (-1) n right? I thought that the exponent of (-1) is n-1 because it changed from n=0 to n=1, and if \((-1)^{n}\), there will be a change of sign between negative sign and positive sign.
asked 2020-11-10
If \(\displaystyle{s}≥{0}\), then \(\displaystyle√{s}^{{2}}\) is equal to
O A. 0
O B. 1
O c. −s
O D. s
...