Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

An irrational number between 5 and 6 is
(a)
(1)/(2)(5+6)
(b)
sqrt(5+6)
(c)
sqrt(5×6)
(d) none of these

An irrational number between $5$ and $6$ is $\newline$ (a) $\frac{1}{2}(5+6)$ $\newline$ (b) $\sqrt{5+6}$ $\newline$ (c) $\sqrt{5 \times 6}$ $\newline$ (d) none of these

View step-by-step help

View step-by-step help

Convert complex numbers between rectangular and polar form

Full solution

Q. An irrational number between

5

and

6

is

\newline

(a)

\frac{1}{2}(5+6)

\newline

(b)

\sqrt{5+6}

\newline

(c)

\sqrt{5 \times 6}

\newline

(d) none of these

Calculate option (a): Calculate option (a): $(\frac{1}{2})(5+6)$ . $(\frac{1}{2})(5+6) = (\frac{1}{2})(11) = 5.5$
Check rationality of $5.5$ : Check if $5.5$ is irrational. $\newline$ $5.5$ can be expressed as a fraction, so it is rational.
Calculate option (b): Calculate option (b): $\sqrt{5+6}$ . $\newline$ $\sqrt{5+6} = \sqrt{11}$
Check irrationality of $\sqrt{11}$ : Check if $\sqrt{11}$ is irrational. $\newline$ $\sqrt{11}$ cannot be expressed as a fraction, so it is irrational.
Calculate option (c): Calculate option (c): $\sqrt{5\times6}$ . $\newline$ $\sqrt{5\times6} = \sqrt{30}$
Check irrationality of $\sqrt{30}$ : Check if $\sqrt{30}$ is irrational. $\newline$ $\sqrt{30}$ cannot be expressed as a fraction, so it is irrational.
Determine irrational numbers: Determine if any of the irrational numbers are between $5$ and $6$ . $\sqrt{11} \approx 3.3166$ and $\sqrt{30} \approx 5.4772$ ; only $\sqrt{30}$ is between $5$ and $6$ .

More problems from Convert complex numbers between rectangular and polar form

Question

Convert the equation to polar form. (Use variables

r

\theta

\newline

y=6x^{2}

Posted 2 months ago

Question

Convert the polar equation

\newline

r=\frac{5}{2\sin \theta-3\cos \theta}

to rectangular form.

Posted 1 month ago

Question

3\left[\cos \left(\frac{\pi}{2}\right)+i \sin \left(\frac{\pi}{2}\right)\right]

in rectangular form.

\newline

Simplify any radicals.

Posted 2 months ago

Question

Find the inverse

\newline

f(x)=\sqrt[3]{2x-7}

Posted 2 months ago

Question

2

1

1

\newline

\newline

\newline

Find the standard form of the equation of the hyperbola with the given characteristics.

\newline

( \pm 6,0)

( \pm 9,0)

Posted 2 months ago

Question

Express as a complex number in simplest a+bi form:

\newline

\frac{6-6 i}{2-i}

\newline

Posted 1 month ago

Question

Express as a complex number in simplest a+bi form:

\newline

\frac{22-24 i}{2-7 i}

\newline

Posted 1 month ago

Question

Express as a complex number in simplest a+bi form:

\newline

\frac{-19-i}{10-9 i}

\newline

Posted 2 months ago

Question

Express as a complex number in simplest a+bi form:

\newline

\frac{-9-6 i}{-5+2 i}

\newline

Posted 1 month ago

Question

Express as a complex number in simplest a+bi form:

\newline

\frac{4-22 i}{2+4 i}

\newline

Posted 1 month ago