Content code
m1037
Slug (identifier)
radical-operations
Parent content
Grades
Secondary III
Secondary IV
Secondary V
Topic
Mathematics
Tags
irrational numbers
irrational
numbers
radical
radicals
decimal numbers
Q'
periodic
repeating
periodicity
non-periodicity
non-repeating
transform a periodic number into a fraction
transformation of a periodic number into a fraction
order in irrational numbers
square roots
cubic roots
irrational numbers and the number line
number line
radicand
rationalization
Content
Contenu
Links
Title (level 2)
Adding Irrational Numbers
Title slug (identifier)
adding-irrational-numbers
Contenu
Title (level 3)
Case 1: Adding Two Radicals With Different Radicands
Title slug (identifier)
case-1
Corps

To be as accurate as possible, we have to leave the operation as is. It is not possible to simplify it further.
It is possible to transform irrational numbers into decimals and add them together. However, we will have to use rounding, which will make the answer less precise.

Content
Corps

|\sqrt{5}+\sqrt{3}|  

|\sqrt{5}+\sqrt{3}\approx2.2361+1.7321\approx3.9682|

Title (level 3)
Case 2: Adding Two Radicals With Identical Radicands
Title slug (identifier)
case-2
Corps

The radicands can be grouped for an exact answer or transformed into decimal numbers.

Content
Corps

|\sqrt{3}+\sqrt{3}=2\sqrt{3}|

or

|\sqrt{3}+\sqrt{3}\approx1.7321+1.7321\approx3.4642|

Title (level 3)
Case 3: Adding Two Irrational Numbers
Title slug (identifier)
case-3
Corps

Whether it is a fraction consisting of the number pi or a radical accompanied by another term, it is necessary to put everything in decimals and then proceed to the addition.

Content
Corps

|\sqrt{2}+\pi\approx1.4142+3.1416\approx4.5558|

Title (level 2)
Subtracting Irrational Numbers
Title slug (identifier)
subtracting-irrational-numbers
Contenu
Corps

When subtracting, we use the same principles as with adding.

Content
Corps

|\sqrt{5}-\sqrt{3}\approx2.2361-1.7321\approx0.5040|

|2\sqrt{3}-\sqrt{3}=\sqrt{3}|
or
|2\sqrt{3}-\sqrt{3}\approx3.4641-1.7321\approx1.7321|

|\pi-\sqrt{2}\approx3.1416-1.4142\approx1.7274|

Title (level 2)
Multiplying Irrational Numbers
Title slug (identifier)
multiplying-irrational-numbers
Contenu
Corps

When multiplying a square root with an identical one, the answer is the value of the radicand.

Content
Corps

|\sqrt{3}\cdot\sqrt{3}=3| 

Corps

If the radicals are different, it suffices to recreate an expression where the two radicands multiply together under the same root.

Content
Corps

|\sqrt{5}\cdot\sqrt{3}=\sqrt{15}|

Title (level 2)
Dividing Irrational Numbers
Title slug (identifier)
dividing-irrational-numbers
Contenu
Corps

When the radical is the same in the numerator and in the denominator, it suffices to reduce them together.

|\frac{\sqrt{2}}{\sqrt{2}}=1|

|\frac{4\sqrt{3}}{2\sqrt{3}}=2|

If the radicals are different, it suffices to create a new fractional expression where the two radicands are found under the same root.

Content
Corps

|\frac{\sqrt{12}}{\sqrt{3}}=\sqrt{\frac{12}{3}}=\sqrt{4}=2|

|\frac{2\sqrt{6}}{\sqrt{2}}=2\sqrt{\frac{6}{2}}=2\sqrt{3}|

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