\(\displaystyle{\left({a}+{10}\right)}{\left({a}+{10}\right)}={a}^{{2}}+{2}{a}{\left({10}\right)}+{10}^{{2}}\)

\(\displaystyle={a}^{{2}}+{20}{a}+{100}\)

\(\displaystyle={a}^{{2}}+{20}{a}+{100}\)

Question

asked 2021-01-13

Simplify the following expression:

\(\displaystyle\frac{{8}}{{{4}-\sqrt{{{6}{n}}}}}\)

\(\displaystyle\frac{{8}}{{{4}-\sqrt{{{6}{n}}}}}\)

asked 2021-01-19

\(\displaystyle\sqrt{{96}}=\sqrt{{4}}\times\sqrt{{48}}\)

\(\displaystyle={2}\times\sqrt{{48}}\)

\(\displaystyle={2}\times\sqrt{{8}}\times\sqrt{{6}}\)

\(\displaystyle={2}\times{4}\times\sqrt{{6}}\)

\(\displaystyle={8}\sqrt{{6}}\)

Is there a mistake in the simplification? What is it? Correct the mistake if there is one and simplify sqrt96.

\(\displaystyle={2}\times\sqrt{{48}}\)

\(\displaystyle={2}\times\sqrt{{8}}\times\sqrt{{6}}\)

\(\displaystyle={2}\times{4}\times\sqrt{{6}}\)

\(\displaystyle={8}\sqrt{{6}}\)

Is there a mistake in the simplification? What is it? Correct the mistake if there is one and simplify sqrt96.

asked 2021-02-11

Consider the following statements. Select all that are always true.

The sum of a rational number and a rational number is rational.

The sum of a rational number and an irrational number is irrational.

The sum of an irrational number and an irrational number is irrational.

The product of a rational number and a rational number is rational.

The product of a rational number and an irrational number is irrational.

The product of an irrational number and an irrational number is irrational.

The sum of a rational number and a rational number is rational.

The sum of a rational number and an irrational number is irrational.

The sum of an irrational number and an irrational number is irrational.

The product of a rational number and a rational number is rational.

The product of a rational number and an irrational number is irrational.

The product of an irrational number and an irrational number is irrational.

asked 2021-02-21

Find the value of the following expression:

\(\displaystyle{4}\sqrt{{2}}+{2}{\left(\sqrt{{36}}-\sqrt{{8}}\right)}\)

\(\displaystyle{4}\sqrt{{2}}+{2}{\left(\sqrt{{36}}-\sqrt{{8}}\right)}\)

asked 2021-01-10

Find the value of the following expression:

\(\displaystyle\frac{{{\sin{{\left({x}\right)}}}}}{{{\cos{{\left(-{x}\right)}}}}}+\frac{{{\sin{{\left(-{x}\right)}}}}}{{{\cos{{\left({x}\right)}}}}}\)

\(\displaystyle\frac{{{\sin{{\left({x}\right)}}}}}{{{\cos{{\left(-{x}\right)}}}}}+\frac{{{\sin{{\left(-{x}\right)}}}}}{{{\cos{{\left({x}\right)}}}}}\)

asked 2021-01-19

\(\displaystyle{Q}:{\quad\text{if}\quad}{\left\lbrace-\frac{{3}}{{4}},\sqrt{{3}},\frac{{3}}{\sqrt{{3}}},\sqrt{{\frac{{25}}{{5}}}},{20},{1.11222},{2.5015132},\ldots,\frac{{626}}{{262}}\right\rbrace}\),

find the following

1) Rational numbers?

2) Irrational numbers?

find the following

1) Rational numbers?

2) Irrational numbers?

asked 2021-02-13

Determine whether the below given statement is true or false. If the statement is false, make the necessary changes to produce a true statement:

All irrational numbers satisfy |x - 4| > 0.

All irrational numbers satisfy |x - 4| > 0.

asked 2021-02-01

Given each set of numbers, list the

a) natural Numbers

b) whole numbers

c) integers

d) rational numbers

e) irrational numbers

f) real numbers

\(\displaystyle{\left\lbrace-{6},\sqrt{{23}},{21},{5.62},{0.4},{3}\frac{{2}}{{9}},{0},-\frac{{7}}{{8}},{2.074816}\ldots\right\rbrace}\)

a) natural Numbers

b) whole numbers

c) integers

d) rational numbers

e) irrational numbers

f) real numbers

\(\displaystyle{\left\lbrace-{6},\sqrt{{23}},{21},{5.62},{0.4},{3}\frac{{2}}{{9}},{0},-\frac{{7}}{{8}},{2.074816}\ldots\right\rbrace}\)

asked 2021-03-12

Find

a) a rational number and

b) a irrational number between the given pair.

\(\displaystyle{3}\frac{{1}}{{7}}\) and \(\displaystyle{3}\frac{{1}}{{6}}\)

a) a rational number and

b) a irrational number between the given pair.

\(\displaystyle{3}\frac{{1}}{{7}}\) and \(\displaystyle{3}\frac{{1}}{{6}}\)

asked 2021-01-23

The rational numbers are dense in \(\displaystyle\mathbb{R}\).
This means that between any two real
numbers a and b with a < b, there exists
a rational number q such that a < q < b.
Using this fact, establish that the
irrational numbers are dense in \(\displaystyle\mathbb{R}\) as
well.